2019
Том 71
№ 10

# Samoilenko A. M.

Articles: 197
Article (Ukrainian)

### Theory of multidimensional Delsarte – Lions transmutation operators. II

Ukr. Mat. Zh. - 2019. - 71, № 6. - pp. 808-839

UDC 517.9
The differential-geometric and topological structures related to the Delsarte transmutation operators and the Gelfand – Levitan – Marchenko equations that describe these operators are studied by using sutable differential de Rham – Hodge – Skrypnik complexes. The correspondence between the spectral theory and special Berezansky-type congruence properties of the Delsarte transmutation operators is established. Some applications to multidimensional differential operators are presented, including the three-dimensional Laplace operator, the two-dimensional classical Dirac operator, and its multidimensional affine extension associated with self-dual Yang – Mills equations. Soliton solutions of a certain class of dynamical systems are discussed.

Article (Ukrainian)

### Form and properties of the canonical Weierstrass product of an entire function with real values on $\mathbb{R}$

Ukr. Mat. Zh. - 2019. - 71, № 5. - pp. 656-662

UDC 517.2
We determine the form and properties of the Weierstrass canonical product of an entire function with real values on $\mathbb{R}$. The proof of the theorem on the order of $R$-integral is specified
[${\it Samoilenko\, A. M.}$ Order and canonical product of the Weierstrass $R$-integral // Ukr. Mat. Zh. — 2019. — ${\bf 71}$, № 4. — P.564-570].

Article (Ukrainian)

### Singular integral equation equivalent in the space of smooth functions to an ordinary differential equation, method of successive approximations for the construction of its smooth solutions and its nonsmooth solutions

Ukr. Mat. Zh. - 2019. - 71, № 4. - pp. 543-563

We propose a singular integral equation whose definition is extended to a singular point by additional conditions. In the space of smooth functions, this equation becomes equivalent, by the indicated extended definition, to an ordinary differential equation, whereas in the space of piecewise discontinuous functions, it becomes equivalent to an impulsive differential equation. For smooth solutions of the singular equation, we substantiate the method of successive approximations. For the ordinary differential equation, this method turns into a new algorithm for the construction of successive approximations. For the investigated equation, we specify a solution of new type, which is equivalent, for the impulsive differential equation, to a solution with discontinuity of the second kind (a “solution with needle”). We propose an algorithmic formula for the general solution of the initial-value problem for the impulsive differential equation.

Article (Ukrainian)

### Order and canonical product of the Weierstrass $R$-integral

Ukr. Mat. Zh. - 2019. - 71, № 4. - pp. 564-570

The order of the $R$-integral is specified and its representation in the form of the canonical Weierstrass product is found.

Anniversaries (Ukrainian)

Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 147-150

Article (Ukrainian)

### Theory of multidimensional Delsarte – Lions transmutation operators. I

Ukr. Mat. Zh. - 2018. - 70, № 12. - pp. 1660-1695

We present a brief review of the original results obtained by the authors in the theory of Delsarte –Lions transmutations of multidimensional spectral differential ope rators based on the classical works by Yu. M. Berezansky, V. A. Marchenko, B. M. Levitan, and R. G. Newton, on the well-known L. D. Faddeev’s survey, the book by L. P. Nyzhnyk, and the generalized De-Rham – Hodge theory suggested by I. V. Skrypnik and developed by the authors for the differential-operator complexes. The operator structure of Delsarte – Lions transformations and the properties of their Volterra factorizations are analyzed in detail. In particular, we study the differential-geometric and topological structures of the spectral properties of the Delsarte – Lions transmutations within the framework of the generalized De-Rham – Hodge theory.

Chronicles (Ukrainian)

### International conference on the mathematical analysis, differential equations, and their applications (MADEA-8) devoted to the 80th birthday of Academician A. M. Samoilenko

Ukr. Mat. Zh. - 2018. - 70, № 10. - pp. 1439-1440

Article (Ukrainian)

### The classical M. A. Buhl problem, its Pfeiffer – Sato solutions and the classical Lagrange – D’Alembert principle for the integrable heavenly type nonlinear equations

Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1652-1689

The survey is devoted to old and recent investigations of the classical M. A. Buhl problem of description of the compatible linear vector field equations and their general M. G. Pfeiffer and modern Lax – Sato-type special solutions. In particular, we analyze the related Lie-algebraic structures and the properties of integrability for a very interesting class of nonlinear dynamical systems called the dispersion-free heavenly type equations, which were introduced by Pleba´nski and later analyzed in a series of articles. The AKS-algebraic and related \scrR -structure schemes are used to study the orbits of the corresponding coadjoint actions, which are intimately connected with the classical Lie – Poisson structures on them. It is shown that their compatibility condition coincides with the corresponding heavenly type equations under consideration. It is also demonstrated that all these equations are originated in this way and can be represented as a Lax compatibility condition for specially constructed loop vector fields on the torus. The infinite hierarchy of conservations laws related to the heavenly equations is described and its analytic structure connected with the Casimir invariants is indicated. In addition, we present typical examples of equations of this kind demonstrating in detail their integrability via the scheme proposed in the paper. The relationship between a very interesting Lagrange – d’Alembert-type mechanical interpretation of the devised integrability scheme and the Lax – Sato equations is also discussed.

Article (Ukrainian)

### A generalized theorem of mean values of an analytic function and an algorism of the determination of mean values

Ukr. Mat. Zh. - 2017. - 69, № 6. - pp. 765-787

We prove the mean-value theorem for functions analytic in starlike domains, propose an algorithm for finding the function of mean values, and study its analytic continuation. We present a differential equation for the function of mean values and the interpretation of the Lagrange formula for analytic functions in terms of the theory of differential equations. The set of points of the initial values of the function of mean values is analyzed and the upper of the radius of expansion of the function of mean values in Taylor’s series is established.

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets’ (on his 75th birthday)

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 579

Anniversaries (Ukrainian)

### On the 100th birthday of outstanding mathematician and mechanic Yurii Oleksiiovych Mytropol’s’kyi (03.01.1917 – 14.06.2008)

Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 132-144

Anniversaries (Ukrainian)

### Volodymyr Leonidovych Makarov (on his 75th birthday)

Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1715-1717

Anniversaries (Ukrainian)

### Mykola Oleksiiovych Perestyuk (on his 70th birthday)

Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 142-144

Anniversaries (Ukrainian)

### Volodymyr Semenovych Korolyuk (on his 90th birthday)

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1151-1152

Article (Ukrainian)

### Dynamical Bifurcation of Multifrequency Oscillations in a Fast-Slow System

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 890-915

We study a dynamical analog of bifurcations of invariant tori for a system of interconnected fast phase variables and slowly varying parameters. It is shown that, in this system, due to the slow evolution of the parameters, we observe the appearance of transient processes (from the damping process to multifrequency oscillations) asymptotically close to motions on the invariant torus.

Anniversaries (Ukrainian)

### Motornyi Vitalii Pavlovych (on his 75th birthday)

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 995-999

Article (Russian)

### Differential Equations with Bistable Nonlinearity

Ukr. Mat. Zh. - 2015. - 67, № 4. - pp. 517-554

We study bounded solutions of differential equations with bistable nonlinearity by numerical and analytic methods. A simple mechanical model of circular pendulum with magnetic suspension in the upper equilibrium position is regarded as a bistable dynamical system simulating a supersensitive seismograph. We consider autonomous differential equations of the second and fourth orders with discontinuous piecewise linear and cubic nonlinearities. Bounded solutions with finitely many zeros, including solitonlike solutions with two zeros and kinklike solutions with several zeros are studied in detail. It is shown that, to within the sign and translation, the bounded solutions of the analyzed equations are uniquely determined by the integer numbers $n=\left[\frac{d}{l}\right]$ where d is the distance between the roots of these solutions and l is a constant characterizing the intensity of nonlinearity. The existence of bounded chaotic solutions is established and the exact value of space entropy is found for periodic solutions.

Anniversaries (Ukrainian)

### On the 100th birthday of O. Yu. Ishlinskii

Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1550-1554

Anniversaries (Ukrainian)

### Yurii Stephanovych Samoilenko (on his 70th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1408-1409

Anniversaries (Ukrainian)

### Major Pylypovych Timan (on his 90th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1141-1144

Anniversaries (Ukrainian)

### Myroslav L’vovych Horbachuk (on his 75 th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454

Article (Russian)

### Dynamics of periodic modes for the phenomenological equation of spin combustion

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 21-43

We consider a scalar parabolic equation in the circle of radius r. This problem is a gasless combustion phenomenological model in the surface of a cylinder of $r$ radius. We consider the problems of the existence, asymptotic form and stability of traveling waves and the nature of gaining, losing their stability.

Anniversaries (Ukrainian)

### Mykola Ivanovych Shkil' (on his 80th birthday)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1720-1722

Chronicles (Ukrainian)

### International conference "Theory of approximation of functions and its applications" dedicated to the 70 th birthday of the corresponding member of NASU Professor O. I. Stepanets (1942 - 2007)

Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1438-1440

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets’ (on the 70 th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 579-581

Anniversaries (Ukrainian)

### Dmytro Ivanovych Martynyuk (on the 70th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 571-573

Anniversaries (Ukrainian)

### Yurii Ivanovych Samoilenko (on the 80th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 574-576

Article (Ukrainian)

### Lipschitzian invariant tori of indefinite monotone system

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 363-383

We consider a nonlinear system in the direct product of a torus and a Euclidean space. For this system, under the conditions of indefinite coercivity and indefinite monotonicity, we establish the existence of a Lipschitzian invariant section.

Article (Ukrainian)

### On asymptotic equivalence of solutions of stochastic and ordinary equations

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1103-1127

For a weakly nonlinear stochastic system, we construct a system of ordinary differential equations the behavior of solutions of which at infinity is similar to the behavior of solutions of the original stochastic system.

Anniversaries (Ukrainian)

### Volodymyr Leonidovych Makarov (on his 70th birthday)

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1135-1136

Obituaries (Ukrainian)

### Anatolii Volodymyrovych Skorokhod

Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 859 -864

Article (English)

### Some problems of the linear theory of systems of ordinary differential equations

Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 237-269

We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet – Lyapunov theory for periodic systems of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula to the introduction of amplitude-phase coordinates in a neighborhood of a periodic trajectory of a dynamical system.

Article (Russian)

### Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 52 - 80

We establish conditions for the existence of solutions vanishing at a singular point for various classes of systems of quasilinear differential equations appearing in the investigation of the asymptotic behavior of solutions of essentially nonlinear nonautonomous differential equations of higher orders.

Article (Russian)

### Optimal control with impulsive component for systems described by implicit parabolic operator differential equations

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1053-1065

We study the problem of optimal control with impulsive component for systems described by abstract Sobolev-type differential equations with unbounded operator coefficients in Hilbert spaces. The operator coefficient of the time derivative may be noninvertible. The main assumption is a restriction imposed on the resolvent of the characteristic operator pencil in a certain right half plane. Applications to Sobolevtype partial differential equations are discussed.

Anniversaries (Ukrainian)

### Life and work of N. N. Bogolyubov (on his 100th birthday)

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1130-1141

Chronicles (Ukrainian)

### Bogolyubov Readings-2008. International Conference "Differential Equations, Theory of Functions and Applications" (on the occasion of the 70th anniversary of academician AM Samoilenko)

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1722

Article (Russian)

### Problem of impulsive regulator for one dynamical system of the Sobolev type

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1027–1034

We establish conditions for the existence of an optimal impulsive control for an implicit operator differential equation with quadratic cost functional. The results obtained are applied to the filtration problem.

Anniversaries (Ukrainian)

### Yuri Yurievich Trokhimchuk (on his 80th birthday)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 701 – 703

Article (Ukrainian)

### Myroslav L’vovych Horbachuk (on his 70th birthday)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442

Anniversaries (Ukrainian)

### Leonіd Andrіyovich Pastur (on his 70th birthday)

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1699-1700

Obituaries (Ukrainian)

### Alexander Ivanovich Stepanets

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1722-1724

Anniversaries (Ukrainian)

### Mark Grigorievich Krein (to the centenary of his birth)

Ukr. Mat. Zh. - 2007. - 59, № 5. - pp. 579-587

Article (Ukrainian)

### On solutions of linear functional differential equations with linearly transformed argument on a semiaxis

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 501–513

We establish conditions under which solutions of a system of linear functional differential equations on a semiaxis are determined as solutions of a certain system of ordinary differential equations.

Anniversaries (Ukrainian)

### Evgen Yakovich Khruslov (on his 75 th birthday)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 549-550

Article (Ukrainian)

### Averaging of initial-value and multipoint problems for oscillation systems with slowly varying frequencies and deviated argument

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 412–430

We prove new theorems on the substantiation of the method of averaging over all fast variables on a segment and a semiaxis for multifrequency systems with deviated argument in slow and fast variables. An algorithm for the solution of a multipoint problem with parameters is studied, and an estimate for the difference of solutions of the original problem and the averaged problem is established.

Chronicles (Ukrainian)

### International Conference "Mathematical Analysis and Differential Equations and Applications"

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 431

Anniversaries (Ukrainian)

### On the 90th birthday of Yurii Alekseevich Mitropol’skii

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Article (Ukrainian)

### Some results of the local theory of smooth functions

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 231–267

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system.

Anniversaries (Ukrainian)

### Yaroslav Borisovich Lopatinsky (09.11.1906 - 03.10.1981)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1443-1445

Obituaries (Ukrainian)

### Andrei Reuter (1937-2006)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1584-1585

Anniversaries (Ukrainian)

### Olexiy Bogolyubov (03.25.1911 - 01.11.2004)

Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 564–567

Anniversaries (Ukrainian)

### Nikolai Perestyuk (60th birthday)

Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 113-114

Anniversaries (Ukrainian)

### Ivan Oleksandrovych Lukovs'kyi (on his 70-th birthday)

Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1418-1419

Anniversaries (Ukrainian)

### Volodymyr Semenovych Korolyuk (the 80th anniversary of his birth)

Ukr. Mat. Zh. - 2005. - 57, № 9. - pp. 1155-1157

Anniversaries (Ukrainian)

### Anatoliy Volodymyrovych Skorokhod (the 75th anniversary of his birth)

Ukr. Mat. Zh. - 2005. - 57, № 9. - pp. 1158-1162

Anniversaries (Ukrainian)

### Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1120-1122

Article (Russian)

### Conditions for Synchronization of One Oscillation System

Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 922–945

Using methods of perturbation theory, we investigate the global behavior of trajectories on a toroidal attractor and in its neighborhood for a system of differential equations that arises in the study of synchronization of oscillations in the mathematical model of an optical laser.

Anniversaries (Ukrainian)

### Yurij Makarovich Berezansky (the 80th anniversary of his birth)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 3-11

Announcement (Ukrainian)

### The Skorobogat'ko international mathematical conference

Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 143-144

Anniversaries (Ukrainian)

### Academician V. Ya. Bunyakovs'kyi (on 200-th anniversary of his birthday)

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1675-1683

Chronicles (Ukrainian)

### The international conference „International workshop on analysis and its applications"

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1722

Chronicles (Ukrainian)

### The fifteenth scientific session of mathematical commission of the Shevchenko Scientific Society

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1584

Article (Ukrainian)

### Truncation method for countable-point boundary-value problems in the space of bounded number sequences

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1203-1230

We consider possible methods for the reduction of a countable-point nonlinear boundary-value problem with nonlinear boundary condition on a segment to a finite-dimensional multipoint problem constructed on the basis of the original problem by the truncation method. The results obtained are illustrated by examples.

Article (Ukrainian)

### Reducibility of a nonlinear oscillation system with pulse influence in the neighborhood of an integral manifold

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1076–1094

In the neighborhood of an asymptotically stable integral manifold of a multifrequency system with pulse influence at fixed times, we perform a decomposition of the equations for angular and position variables.

Obituaries (Ukrainian)

### Anatolii Yakovych Dorogovtsev

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1151-1152

Anniversaries (Ukrainian)

### On the 70th anniversary of the Institute of Mathematics of the Ukrainian National Academy of Sciences

Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 723–736

Anniversaries (Ukrainian)

### V. G. Georgii Mykolaiovych Polozhyi (on his 90th birthday)

Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 560-561

Anniversaries (Ukrainian)

### Dmytro Yakovych Petryna (on his 70 th birthday)

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 291-292

Article (English)

### Hopf Algebras and Integrable Flows Related to the Heisenberg–Weil Coalgebra

Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 88-96

On the basis of the structure of Casimir elements associated with general Hopf algebras, we construct Liouville–Arnold integrable flows related to naturally induced Poisson structures on an arbitrary coalgebra and their deformations. Some interesting special cases, including coalgebra structures related to the oscillatory Heisenberg–Weil algebra and integrable Hamiltonian systems adjoint to them, are considered.

Article (Ukrainian)

### Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory

Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1704-1719

On the basis of generalized Lagrange identity for pairs of formally adjoint multidimensional differential operators and a special differential geometric structure associated with this identity, we propose a general scheme of the construction of corresponding transformation operators that are described by nontrivial topological characteristics. We construct explicitly the corresponding integro-differential symbols of transformation operators, which are used in the construction of Lax-integrable nonlinear two-dimensional evolutionary equations and their Darboux–Bäcklund-type transformations.

Article (Russian)

### On One Sequence of Polynomials and the Radius of Convergence of Its Poisson–Abel Sum

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 926-934

For one sequence of polynomials arising in the construction of the numerical-analytic method for finding periodic solutions of nonlinear differential equations, we determine the explicit form of the Poisson–Abel sum and the exact solution of the equation for finding the radius of convergence of this sum.

Article (Russian)

### On One Problem of the Investigation of Global Solutions of Linear Differential Equations with Deviating Argument

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 631-640

We present conditions under which global solutions of linear systems of differential equations with deviating argument are solutions of ordinary differential equations.

Article (Ukrainian)

### Construction of an Integral Manifold of a Multifrequency Oscillation System with Fixed Times of Pulse Action

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 641-662

We determine a class of multifrequency resonance systems with pulse action for which an integral manifold exists. We construct a function that determines a discontinuous integral manifold and investigate its properties.

Article (Ukrainian)

### Error Estimates for the Averaging Method for Pulse Oscillation Systems

Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 510-524

We prove new theorems on the justification of the averaging method on a segment and semiaxis in multifrequency oscillation systems with pulse action at fixed times.

Article (English)

### Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 66-74

We analyze the geometric structure of the Lyapunov–Schmidt approach to studying critical manifolds of weakly perturbed Lagrangian and Hamiltonian systems.

Article (Russian)

### Vladimir Nikolaevich Koshlyakov (On His 80th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1587-1588

Anniversaries (Ukrainian)

### Mykola Ivanovych Shkil' (On His 70th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1589-1591

Article (Russian)

### On the Asymptotic Integration of a System of Linear Differential Equations with a Small Parameter in the Coefficients of a Part of Derivatives

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1505-1517

We propose an asymptotic method for the integration of one type of systems of linear differential equations with a small parameter in the coefficients of a part of derivatives.

Article (Russian)

### Solutions of Weakly-Perturbed Linear Systems Bounded on the Entire Axis

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1517-1530

We establish conditions under which solutions of weakly-perturbed systems of linear ordinary differential equations bounded on the entire axis R emerge from the point ε = 0 in the case where the corresponding unperturbed homogeneous linear differential system is exponentially dichotomous on the semiaxes R + and R .

Article (Ukrainian)

### International Scientific Conference on the Theory of Evolution Equations (Fifth Bogolyubov Readings)

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1440

Article (Ukrainian)

### Averaging of Boundary-Value Problems with Parameters for Multifrequency Impulsive Systems

Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1237-1249

By using the averaging method, we prove the solvability of boundary-value problems with parameters for nonlinear oscillating systems with pulse influence at fixed times. We also obtain estimates for the deviation of solutions of the averaged problem from solutions of the original problem.

Article (Ukrainian)

### Singularly Perturbed Equations with Impulse Action

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1089-1009

We propose and justify an algorithm for the construction of asymptotic solutions of singularly perturbed differential equations with impulse action.

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets' (on his 60-th birthday)

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 579-580

Anniversaries (Ukrainian)

### Mykhailo Iosypovych Yadrenko (On His 70th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 435-438

Article (Russian)

### On Invariant Tori of Itô Stochastic Systems

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 501-513

By using the Green–Samoilenko function, we establish conditions for the existence of invariant sets of Itô stochastic systems that are extensions of dynamical systems on a torus.

Chronicles (Ukrainian)

### International scientific conference "New approaches to the solution of differential equations"

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 575-576

Anniversaries (Ukrainian)

### Dmytro Ivanovych Martynyuk (On the 60th Anniversary of His Birth)

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 291-292

Article (Ukrainian)

### On Some Properties of the Behavior of Linear Extensions of Dynamical Systems on a Torus under Perturbation of Phase Variables

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 408-412

We investigate classes of linear extensions of dynamical systems on a torus for which the Lyapunov functions exist for an arbitrary flow on the torus. Linear extensions for which the Lyapunov functions exist only with varying coefficients are considered separately. We investigate the problem of preservation of regularity under perturbation of phase variables.

Anniversaries (Ukrainian)

### Mykola Ivanovych Portenko (On His 60th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 147-148

Anniversaries (Ukrainian)

### Mykhailo Vasyl'ovych Ostrograds'kyi and his role in the development of mathematics

Ukr. Mat. Zh. - 2001. - 53, № 8. - pp. 1011-1023

Article (Russian)

### On the Existence of Periodic Solutions for Certain Classes of Systems of Differential Equations with Random Pulse Influence

Ukr. Mat. Zh. - 2001. - 53, № 8. - pp. 1061-1079

We establish conditions for the existence of periodic solutions for systems of differential equations with random right-hand side and random pulse influence at fixed times. We consider the case of small pulse perturbation and weakly nonlinear systems.

Article (Russian)

### On the Existence of a Unique Green Function for the Linear Extension of a Dynamical System on a Torus

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 513-521

We prove two theorems on the existence of a unique Green function for a linear extension of a dynamical system on a torus. We also give two examples of the construction of this function in explicit form.

Anniversaries (Russian)

### Naum Il'ich Akhiezer (on his 100-th birthday)

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 291-293

Article (Ukrainian)

### Oleksii Mykolajovych Boholyubov (on His 90th Birthday)

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 294-295

Article (Russian)

### On the Exponential Dichotomy on $\mathbb{R}$ of Linear Differential Equations in $\mathbb{R}^n$

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 356-371

New results of the investigation of exponential dichotomy on the entire axis of linear differential equations in $\mathbb{R}^n$ are presented.

Anniversaries (Ukrainian)

### Igor Volodymyrovych Skrypnik (On His 60th Birthday)

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1443-1445

Anniversaries (Ukrainian)

### Anatolii Vladimirovich Skorokhod (On His 70th Birthday)

Ukr. Mat. Zh. - 2000. - 52, № 9. - pp. 1155-1157

Anniversaries (Ukrainian)

### On the 75th Birthday of Vladimir Semenovich Korolyuk

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1011-1013

Anniversaries (Ukrainian)

### Yurii Makarovich Berezanskii

Ukr. Mat. Zh. - 2000. - 52, № 5. - pp. 579-581

Article (Russian)

### On the 80th birthday of Academician N. P. Korneichuk

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 3-4

Article (Ukrainian)

### Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable Hamiltonian systems. II

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1513–1528

By using the Cartan differential-geometric theory of integral submanifolds (invariant tori) of completely Liouville—Arnold integrable Hamiltonian systems on the cotangent phase space, we consider an algebraic-analytical method for the investigation of the corresponding mapping of imbedding of an invariant torus into the phase space. This enables one to describe analytically the structure of quasiperiodic solutions of the Hamiltonian system under consideration. We also consider the problem of existence of adiabatic invariants associated with a slowly perturbed Hamiltonian system.

Article (Ukrainian)

### Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable hamiltonian systems. I

Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1379–1390

By using the Cartan differential-geometric theory of integral submanifolds (invariant tori) of completely Liouville-Arnol’d integrable Hamiltonian systems on the cotangent phase space, we consider an algebraic-analytic method for the investigation of the corresponding mapping of imbedding of an invariant torus into the phase space. This enables one to describe analytically the structure of quasiperiodic solutions of the Hamiltonian system under consideration.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. VII

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1244–1261

For the numerical-analytic method suggested by A. M. Samoilenko in 1965, we analyze the application to abstract differential equations, implicit equations, and control problems.

Brief Communications (Russian)

### On invariant tori of countable systems of differential equations with delay

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1292–1295

We obtain conditions for the existence and smoothness of invariant tori of countable systems of differential equations with delay.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. VI

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 960–971

We analyze the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary-value problems.

Article (Ukrainian)

### On periodic solutions of the equation of a nonlinear oscillator with pulse influence

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 827–834

We study periodic solutions and the behavior of phase trajectories of the differential equation of a nonlinear oscillator with pulse influence at unfixed moments of time.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. V

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 663–673

We analyze the application of the numerical-analytic method proposed by A. M. Samoilenko in 1965 to difference equations.

Article (Russian)

### Discrete dynamical systems with invariant asymptotically stable toroidal manifold

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 466–471

We obtain conditions for asymptotic stability of quasiperiodic trajectories of discrete dynamical systems in the case of infinite-dimensional Banach space.

Article (Ukrainian)

### On analytic solutions of nonlinear differential functional equations with nonlinear deviations of arguments

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 234–240

We obtain the conditions for existence and uniqueness of an analytic solution of a nonlinear differential functional equation with nonlinear deviations of the argument

Article (Ukrainian)

### Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced system

Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 78–97

We present a spatially two-dimensional generalization of the hierarchy of Kadomtsev-Petviashvili equations under nonlocal constraints (the so-called 2-dimensionalk-constrained KP-hierarchy, briefly called the 2d k-c-hierarchy). As examples of (2+1)-dimensional nonlinear models belonging to the 2d k-c KP-hierarchy, both generalizations of already known systems and new nonlinear systems are presented. A method for the construction of exact solutions of equations belonging to the 2d k-c KP-hierarchy is proposed.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. IV

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1656–1672

We analyze the application of the numerical-analytic method proposed by Samoilenko in 1965 to autonomous systems of differential equations and impulsive equations.

Article (Russian)

### Asymptotic method for the investigation of m-frequency oscillation systems

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1366–1387

We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of decomposable m-frequency oscillation systems.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. III

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 960–979

We analyze results concerning the application of the numerical-analytic method suggested by Samoilenko to delay differential equations, differential equations with “maxima,” functional-differential, operator-differential, and integro-differential equations.

Article (Ukrainian)

### On the smoothness of the Green function for the problem of bounded invariant manifolds

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 570–584

We investigate the smoothness of the Green function for the problem of bounded invariant manifolds of linear extensions of dynamical systems.

Chronicles (Ukrainian)

### The Third Bogolyubov Readings. International Scientific Conference “Asymptotic and Qualitative Methods in the Theory of Nonlinear Oscillations”

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 599

Chronicles (Ukrainian)

### All-Ukrainian scientific conference “New approaches to the solution of differential equations”

Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 454–455

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. II

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 225–243

We analyze results concerning the application of the numerical-analytic method suggested by Samoilenko in 1965 to second-order differential equations.

Article (Russian)

### Invariant tori of linear countable systems of discrete equations given on an infinite-dimensional torus

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 244–251

We study the problem of existence and uniqueness of invariant toroidal manifolds of countable systems of linear equations given on an infinite-dimensional torus.

Article (Russian)

### Invariant tori of differential equations in a Banach space

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 13–21

We establish conditions for the existence, uniqueness, and smoothness of the toroidal manifolds of differential equations with unbounded operator coefficients.

Article (Russian)

### The theory of the numerical-analytic method: Achievements and new trends of development. I

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 102–117

We describe the history of the development of the numerical-analytic method suggested by Samoilenko in 1965 and analyze the relation of this method to other investigations.

Article (Russian)

### Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1661–1676

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients.

Article (Russian)

### On V.N. Koshlyakov’s works in mechanics and its applications

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1444–1453

We present a survey of the principal results obtained by V. N. Koshlyakov in analytical mechanics, dynamics of solids, and applied theory of gyroscopes.

Anniversaries (Ukrainian)

### Bohdan Iosypovych Ptashnyk

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1155–1156

Chronicles (Ukrainian)

### Seminar-School “Mathematical Simulation”

Ukr. Mat. Zh. - 1997. - 49, № 8. - pp. 1152

Article (Ukrainian)

### Boundary-value problems with parameters for a multifrequency oscillation system

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 581–589

By using the averaging method, we prove the solvability of boundary-value problems with parameters for nonlinear oscillation systems. We obtain estimates for the deviation of solutions of averaged problems from solutions of original problems.

Chronicles (Ukrainian)

### Ukrainian school-seminar "Nonlinear boundary value problems of mathematical physics and applications"

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 613–617

Anniversaries (Ukrainian)

### Yurii L’vovich Daletskii

Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 323–325

Article (Russian)

### Weakly nonlinear boundary-value problems for operator equations with pulse influence

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 272–288

We consider the problem of finding conditions of solvability and algorithms for construction of solutions of weakly nonlinear boundary-value problems for operator equations (with the Noetherian linear part) with pulse influence at fixed times. The method of investigation is based on passing by methods of the Lyapunov—Schmidt type from a pulse boundary-value problem to an equivalent operator system that can be solved by iteration procedures based on the fixed-point principle.

Article (Ukrainian)

### On the contribution of Yu. A. Mitropol’skii to the development of asymptotic methods in nonlinear mechanics

Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 5–10

We present a survey of the most important scientific results of Yu. A. Mitropol’skii in the fields of nonlinear differential equations, mathematical physics,and the theory of nonlinear oscil.

Article (Ukrainian)

### Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds

Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 122–140

We investigate S1-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows.

Anniversaries (Ukrainian)

### Wilhelm Illich Fushchych (on his 60th birthday)

Ukr. Mat. Zh. - 1996. - 48, № 12. - pp. 1587-1588

Anniversaries (Ukrainian)

### Yurii Dmitrievich Sokolov (on his 100th birthday)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1443-1445

Brief Communications (Ukrainian)

### Boundary-Value problems for systems of integro-differential equations with Degenerate Kernel

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1576-1579

By using methods of the theory of generalized inverse matrices, we establish a criterion of solvability and study the structure of the set of solutions of a general linear Noether boundary-value problem for systems of integro-differential equations of Fredholm type with degenerate kernel.

Article (Ukrainian)

### Averaging method in multipoint problems of the theory of nonlinear oscillations

Ukr. Mat. Zh. - 1996. - 48, № 8. - pp. 1096-1103

By using the averaging method, we prove the solvability of multipoint problems for nonlinear oscillation systems and estimate the deviation of solutions of original and averaged problems.

Chronicles (Ukrainian)

### School-Seminar “Nonlinear boundary-value problems in Mathematical Physics and their applications”

Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 863-865

Anniversaries (Ukrainian)

### Evgenii Yakovlevich Remez

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 285-286

Article (Russian)

### On the reducibility of countable systems of linear difference equations

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1533–1541

We solve the problem of reducibility of a countable linear system of standard difference equations with unbounded right-hand sides by the method of construction of iterations with accelerated convergence. For systems of this type with bounded right-hand sides, this problem is reduced to a finite-dimensional case.

Anniversaries (Ukrainian)

### On the 60th birthday of Leonid Pavlovich Nizhnik

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1416–1417

Anniversaries (Ukrainian)

### Ivan Aleksandrovich Lukovskii (on his 60th birthday)

Ukr. Mat. Zh. - 1995. - 47, № 8. - pp. 1136-1137

Article (Ukrainian)

### On the integral of a function along the trajectories of a nilpotent flow

Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 837–847

We establish conditions under which the integral of a function along a nilpotent flow on the Heisenberg-Iwasawa manifold increases not faster than $|t|^{1/2+ ε},\; 0 < ε < 1$ and indicate cases where this integral can be represented as a superposition of a function defined on a nilmanifold and a nilpotent flow.

Article (Russian)

### On some problems in perturbation theory of smooth invariant tori of dynamical systems

Ukr. Mat. Zh. - 1994. - 46, № 12. - pp. 1665–1699

Problems related to perturbation theory of smooth invariant tori of dynamical systems in a n-dimensional Euclidean spaceR n are considered. The clarification of these problems plays an important role for perturbation theory suggested by the author in [1] and extends the scope of its application.

Brief Communications (Russian)

### Solutions of systems of nonlinear difference-differential equations of neutral type asymptotically bounded in the entire axis

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1597-1601

For a certain class of systems of difference-differential equations of neutral type, we study the properties of solutions asymptotically bounded on the entire axis.

Article (Ukrainian)

### Institute of Mathematics of The Ukrainian National Academy of Sciences: 60 years of development

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1291–1303

In this brief historical essay, we describe main stages of the formation and development of the Institute of Mathematics of the Ukrainian National Academy of Sciences from its foundation in 1934 till now. Our attention is mainly focused on the achievements of its leading scientists and main directions of mathematical researches carried out in the Institute of Mathematics.

Article (Russian)

### Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1399–1408

A dynamical system is studied in the neighborhood of an invariant toroidal manifold for the most general relationship between the dimensionality of the phase space and the dimensionality of the manifold.

Article (Ukrainian)

### Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1216–1223

Brief Communications (Ukrainian)

### To the memory of Valentin Anatol'evich Zmorovich

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1110–1111

Article (Russian)

### Solutions of systems of nonlinear functional-differential equations bounded in the entire real axis and their properties

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 737–747

For a system of nonlinear functional-differential equations with a linearly transformed argument, we establish the existence and uniqueness conditions for a solution bounded in the entire real axis and study the properties of this solution.

Article (Russian)

### Reducibility of nonlinear almost periodic systems of difference equations given on a torus

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 404–412

Sufficient conditions are established for the reducibility of a nonlinear system of difference equations $$x(x + 1) = x(1) + \omega + P(x(t), t) + \lambda,$$ where $P(x, t)$ is a function $2\pi$-periodic in $x_i(i = 1,..., n)$ and almost periodic in $t$ with a frequency basis $\alpha$, to the system $$y(t + 1) = y(t) + \omega.$$

Chronicles (Ukrainian)

### The conference “Nonlinear problems of differential equations and mathematical physics. The second Bogolyubov readings”

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 471

Article (Ukrainian)

### The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1668–1681

On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered for a system on a plane.

Article (Russian)

### On decomposability of countable systems of differential equations

Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1424–1432

Conditions under which there exists a change of variables that decomposes a countable system of differential equations are established for the entire real axis and a semiaxis. Similar problems are investigated for a countable system with pulse influence.

Article (Ukrainian)

### Study of a discrete dynamic system in a neighborhood of a quasi-periodic trajectory

Ukr. Mat. Zh. - 1992. - 44, № 12. - pp. 1702–1711

Obituaries (Ukrainian)

### An issue dedicated to the illustrious memory of Mykol Mykolayovych Bogolyubov

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1155-1156

Article (Ukrainian)

### Spaces of piecewise-continuous almost-periodic functions and of almost-periodic sets on the line. I

Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1613–1619

Anniversaries (Ukrainian)

### Parasyuk Ostap Stepanovich (his 70th birthday)

Ukr. Mat. Zh. - 1991. - 43, № 11. - pp. 1443-1444

Article (Ukrainian)

### Dynamic systems in $\mathcal{T}_m \times E^n$

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 723–727

Article (Ukrainian)

### Unbounded functions with almost periodic differences

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1409–1413

Article (Ukrainian)

### Justification of a numerical-analytic method of successive approximations for problems with integral boundary conditions

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1231–1239

Brief Communications (Russian)

### Otto Yul'evich Shmidt (on the occasion of his 100th birthday)

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 867–869

Article (Ukrainian)

### Generalized solutions of impulse systems and the phenomenon of pulsations

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 657–663

Article (Ukrainian)

### Study of a dynamical system in a neighborhood of an invariant toroidal manifold

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 530-537

Article (Ukrainian)

### An averaging principle for a class of systems of differential equations with deviating argument

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1363–1369

Article (Ukrainian)

### Reducibility of a system of linear differential equations with quasiperiodic coefficients

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1669–1680

Brief Communications (Russian)

### N. N. Bogolyubov's research in mathematics and theoretical physics

Ukr. Mat. Zh. - 1989. - 41, № 9. - pp. 1156–1164

Article (Ukrainian)

### Method of averaging in multifrequency systems with slowly varying parameters

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 493-500

Article (Ukrainian)

### The infinite-dimensional Schrodinger operator and its potential perturbations

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 97-105

Article (Ukrainian)

### The development of methods of nonlinear mechanics in the works of Yu. A. Mitropol'skii

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 534–538

Article (Ukrainian)

### Smoothness in the parameter of an invariant torus of a quasilinear system of differential equations

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 605–618

Article (Ukrainian)

### Stability of certain two-particle systems

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 128–131

Article (Ukrainian)

### Splitting of a system of differential equations with slowly varying phase in the neighborhood of an asymptotically stable invariant torus

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 751–756

Article (Ukrainian)

### Averaging method in systems with impulses

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 56 – 64

Article (Ukrainian)

### Certain iteration methods for the determination of periodic solutions of nonautonomous systems of differential equations

Ukr. Mat. Zh. - 1984. - 36, № 3. - pp. 346 - 352

Article (Ukrainian)

### Decomposability of linearized systems of differential equations

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 587-593

Article (Ukrainian)

### Periodic and almost-periodic solutions of impulsive differential equations

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 66-73

Article (Ukrainian)

### Numerical-analytic method for solving boundary-value problems for ordinary differential equations

Ukr. Mat. Zh. - 1981. - 33, № 4. - pp. 467–475

Article (Ukrainian)

### Separatrice manifolds and decomposability of a linear extension of a dynamical system on the torus

Ukr. Mat. Zh. - 1981. - 33, № 1. - pp. 31-38

Article (Ukrainian)

### Green's function of a linear extension of a dynamic system on a torus, its conditions of uniqueness and the properties following from them

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 791–797

Article (Ukrainian)

### A numerical-analytic method for autonomous systems with a small perturbation

Ukr. Mat. Zh. - 1979. - 31, № 2. - pp. 214–220

Article (Ukrainian)

### Asymptotic expansions in nonlinear mechanics

Ukr. Mat. Zh. - 1979. - 31, № 1. - pp. 42–53

Article (Ukrainian)

### Continuity of Green's function for the invariant torus problem

Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 779–788

Article (Ukrainian)

### The problem of justifying the averaging method for second-order equations with impulsive action

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp. 750–762

Article (Ukrainian)

### Splitting of a dynamical system in the neighborhood of a stable invariant manifold

Ukr. Mat. Zh. - 1977. - 29, № 4. - pp. 555–560

Article (Ukrainian)

### Multifrequency oscillations of weakly nonlinear second-order systems

Ukr. Mat. Zh. - 1976. - 28, № 6. - pp. 745–762

Article (Ukrainian)

### On asymptotic integration of weakly nonlinear systems

Ukr. Mat. Zh. - 1976. - 28, № 4. - pp. 483–500

Article (Ukrainian)

Ukr. Mat. Zh. - 1975. - 27, № 4. - pp.

Article (Ukrainian)

### On the existence of the Green function of the problem of the invariant torus

Ukr. Mat. Zh. - 1975. - 27, № 3. - pp. 348–359

Article (Russian)

### Existence of invariant manifolds of systems with delay

Ukr. Mat. Zh. - 1974. - 26, № 5. - pp. 611–620

Article (Ukrainian)

### The method of averaging in systems with an impulsive action

Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 411–418

Article (Ukrainian)

### Invariant sets of systems with instantaneous changes in standard form

Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 129-134

Article (Ukrainian)

### Projection method for equations with nonpotential operators

Ukr. Mat. Zh. - 1972. - 24, № 3. - pp. 373—383

Article (Ukrainian)

### Quasi-periodic oscillations in linear systems

Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 180—193

Article (Ukrainian)

### Averaging method for investigating systems subjected to an impulsive action

Ukr. Mat. Zh. - 1967. - 19, № 5. - pp. 96–104

Article (Russian)

### On the construction of solutions of linear differential equations with quasiperiodic coefficients by the method of accelerated convergence

Ukr. Mat. Zh. - 1965. - 17, № 6. - pp. 42-59

Article (Russian)

### Numerical analytical method of investigating periodic systems of ordinary differential equations. I

Ukr. Mat. Zh. - 1965. - 17, № 4. - pp. 82-93

Brief Communications (Russian)

### On periodic solutions of differential equations with undifferentiable right parts

Ukr. Mat. Zh. - 1963. - 15, № 3. - pp. 328-332

Article (Russian)

### On a case of continuous dependence of the solutions of differencial equations on the parameter

Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 289-298

A theorem is proved on the continuous dependence on the parameter of solutions of the integral equation (1.1). It is used for the investigation of the dependence on the parameter of the solution of a differential equation in respect to which the right side is continuous in the integral sense, and for finding the limiting function to the solutions.

Brief Communications (Russian)

### Application of the averaging method for the investigation of oscillations, induced by instantaneous impulses, in self-oscillating systems of the second order with a small parameter

Ukr. Mat. Zh. - 1961. - 13, № 3. - pp. 103-110