2019
Том 71
№ 11

# Mitropolskiy Yu. A.

Articles: 180
Anniversaries (Ukrainian)

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

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

Anniversaries (Ukrainian)

### Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

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 (Russian)

### Aleksandr Mikhailovich Lyapunov (the 150th anniversary of his birth)

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 996-1000

Anniversaries (Ukrainian)

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

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

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

Article (Ukrainian)

### Conditions for the Existence of Solutions of a Periodic Boundary-Value Problem for an Inhomogeneous Linear Hyperbolic Equation of the Second Order. I

Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 912–921

We consider the periodic boundary-value problem $u_{tt} − u_{xx} = g(x, t),\; u(0, t) = u(π, t) = 0,\; u(x, t + ω) = u(x, t)$. By representing a solution of this problem in the form $u(x, t) = u^0(x, t) + ũ(x, t)$, where $u^0(x, t)$ is a solution of the corresponding homogeneous problem and $ũ(x, t)$ is the exact solution of the inhomogeneous equation such that $ũ(x, t + ω) u_x = ũ(x, t)$, we obtain conditions for the solvability of the inhomogeneous periodic boundary-value problem for certain values of the period ω. We show that the relation obtained for a solution includes known results established earlier.

Brief Communications (Russian)

### Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry

Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 997–1001

By using the method of a priori estimates, we establish differential inequalities for energetic norms in $W^l_{2,r}$ of solutions of problems with a free bound in media with the fractal geometry for one-dimensional evolutionary equation. On the basis of these inequalities, we obtain estimates for the stabilization time $T$.

Anniversaries (Ukrainian)

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

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

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

Brief Communications (Ukrainian)

### On the Application of the Averaging Principle in Stochastic Differential Equations of Hyperbolic Type

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 711-715

We prove a theorem on the application of the Bogolyubov–Mitropol'skii averaging principle to stochastic partial differential equations of the hyperbolic type.

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

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

Anniversaries (Ukrainian)

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

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

Anniversaries (Ukrainian)

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

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

Article (Russian)

### On One Nonlocal Problem with Free Boundary

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 908-918

We investigate group-theoretic properties of a nonlocal problem with free boundary for a degenerating quasilinear parabolic equation. We establish conditions for the invariant solvability of this problem, perform its reduction, and obtain an exact self-similar solution.

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

Anniversaries (Ukrainian)

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

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

Anniversaries (Russian)

### On the Scientific, Pedagogic, and Public Activities of Academician Mikhail Alekseevich Lavrent'ev at the Ukrainian Academy of Sciences (1939–1949) (on the 100th Anniversary of the Birth of M. A. Lavrent'ev)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1312-1321

Article (Ukrainian)

### Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 931-935

On the basis of the exact solution of the linear Dirichlet problem $u_{tt} - u_{xx} = f\left( {x,t} \right)$ , $u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,$ $0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \leqslant 2\pi ,$ we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u ttu xx = f(x, t, u, u t).

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

Anniversaries (Russian)

### On the 90th Anniversary of the Birth of Academician N.N. Bogolyubov

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1012–1013

Article (Ukrainian)

### On the role of N.N. Bogolyubov in the development of the theory of nonlinear oscillations

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1014–1035

A review of N. N. Bogolyubov's works on investigations in the theory of nonlinear oscillations is presented.

Anniversaries (Ukrainian)

### 50 Years of “Ukrainskii Matematicheskii Zhurnal”

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 579–580

Article (Russian)

### Stabilization for a finite time in problems with free boundary for some classes of nonlinear second-order equations

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 214–223

We obtain estimates for the time of stabilization of solutions of problems with free boundary for one-dimensional quasilinear parabolic equations.

Article (Russian)

### Random oscillations in the Van der Pol system under the action of a broadband random process

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1517–1521

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process.

Anniversaries (Russian)

### On the 85th birthday of Alexandr Yul’evich Ishlinskii

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1416–1418

Article (Russian)

### Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 818–821

On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ .

Article (Ukrainian)

### On the application of Ateb-functions to the construction of an asymptotic solution of the perturbed nonlinear Klein-Gordon equation

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 665–670

For the perturbed nonlinear Klein-Gordon equation, we construct an asymptotic solution by using Ateb-functions. We consider autonomous and nonautonomous cases.

Anniversaries (Ukrainian)

### Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Article (Russian)

### On the construction of an asymptotic solution of a perturbed Bretherton equation

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 58–71

We consider the application of the asymptotic method of nonlinear mechanics to the construction of the first and second approximations of a solution of the Bremerton equation.

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.

Article (Ukrainian)

### Problems with free boundaries for nonlinear parabolic equations

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1360–1372

We establish necessary conditions for the existence of effects of space localization and stabilization in time that are qualitatively new for evolutionary equations. We suggest constructive methods for the solution of the corresponding one-dimensional problems with free boundaries that appear in ecology and medicine.

Anniversaries (Ukrainian)

### Bohdan Iosypovych Ptashnyk

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

Article (Ukrainian)

### A periodic problem for the inhomogeneous equation of string oscillations

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 558–565

We study a periodic problem for the equation u tt−uxx=g(x, t), u(x, t+T)=u(x, t), u(x+ω, t)= =u(x, t), ℝ2 and establish conditions of the existence and uniqueness of the classical solution.

Anniversaries (Ukrainian)

### Yurii L’vovich Daletskii

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

Article (Russian)

### Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 244–254

We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.

Article (Ukrainian)

### Problems with free boundaries and nonlocal problems for nonlinear parabolic equations

Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 84–97

We present statements of problems with free boundaries and nonlocal problems for nonlinear parabolic equations arising in metallurgy, medicine, and ecology. We consider some constructive methods for their solution.

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

Article (Russian)

### Space-time localization in problems with free boundaries for a nonlinear second-order equation

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 202-211

For thermal and diffusion processes in active media described by nonlinear evolution equations, we study the phenomena of space localization and stabilization for finite time.

Anniversaries (Ukrainian)

### Evgenii Yakovlevich Remez

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

Anniversaries (Ukrainian)

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

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

Article (Russian)

### On construction of asymptotic solution of the perturbed Klein-Gordon equation

Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1209-1216

We consider an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation.

Article (English)

### Bogolyubov averaging and normalization procedures in nonlinear mechanics. IV

Ukr. Mat. Zh. - 1995. - 47, № 8. - pp. 1044–1068

In this paper, we apply the theory developed in parts I-III [Ukr. Math. Zh.,46, No. 9, 1171–1188; No. 11, 1509–1526; No. 12, 1627–1646 (1994)] to some classes of problems. We consider linear systems in zero approximation and investigate the problem of invariance of integral manifolds under perturbations. Unlike nonlinear systems, linear ones have centralized systems, which are always decomposable. Moreover, restrictions connected with the impossibility of diagonalization of the coefficient matrix in zero approximation are removed. In conclusion, we apply the method of local asymptotic decomposition to some mechanical problems.

Anniversaries (Ukrainian)

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

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

Article (Russian)

### On a nonlocal problem for a parabolic equation

Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 790–800

We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW 2 1,0 (Q T ), and construct a difference scheme for the second-order approximation.

Article (Russian)

### Approximate solution of the Fokker-Planck-Kolmogorov equation

Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 351–361

For the Fokker-Planck-Kolmogorov equation, the higher approximations are constructed by using the Bogolyubov averaging method.

Article (English)

### Bogolyubov averaging and normalization procedures in nonlinear mechanics. III

Ukr. Mat. Zh. - 1994. - 46, № 12. - pp. 1627–1646

We describe the technique of normalization based on the method of asymptotic decomposition in the space of representation of a finite-dimensional Lie group. The main topics of the theory necessary for understanding the method are outlined. Models based on the Van der Pol equation are investigated by the method of asymptotic decomposition in the space of homogeneous polynomials (the space of representation of a general linear group in a plane) and in the space of representation of a rotation group on a plane (ordinary Fourier series). The comparison made shows a dramatic decrease in the necessary algebraic manipulations in the second case. We also discuss other details of the technique of normalization based on the method of asymptotic decomposition.

Article (English)

### Bogolyubov averaging and normalization procedures in nonlinear mechanics. II

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1509–1526

By using a new method suggested in the first part of the present work, we study systems which become linear in the zero approximation and have perturbations in the form of polynomials. This class of systems has numerous applications. The following fact is even more important: Our technique demonstrates how to generalize the classical method of Poincaré-Birkhoff normal forms and obtain new results by using group-theoretic methods. After a short exposition of the general theory of the method of asymptotic decomposition, we illustrate the new normalization technique as applied to models based on the Lotka-Volterra equations.

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 (Ukrainian)

### Bogolyubov averaging and normalization procedures in nonlinear mechanics. I

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1171–1188

We suggest a new method for asymptotic analysis of nonlinear dynamical systems based on group-the-oretic methods. On the basis of the Bogolyubov averaging method, we develop a new normalization procedure — “asymptotic decomposition.” We clarify the contribution of this procedure to the interpretation and development of the averaging method for systems in the standard form and systems with several fast variables. According to this method, the centralized system is regarded as a direct analog of the system averaged in Bogolyubov's sense. The operation of averaging is interpreted as the Bogolyubov projector, i.e., the operation of projection of an operator onto the algebra of centralizer.

Article (Russian)

### Asymptotic methods in the theory of nonlinear random oscillations

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1011–1016

We study applications of asymptotic methods of nonlinear mechanics and the method of Fokker-Planck-Kolmogorov equations to the investigation of random multifrequency oscillations in systems with many degrees of freedom.

Brief Communications (Ukrainian)

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

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

Chronicles (Ukrainian)

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

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

Anniversaries (Russian)

### Mark Grigor'evich Krein

Ukr. Mat. Zh. - 1994. - 46, № 1-2. - pp. 3–4

Article (Russian)

### Reducibility of linear systems of difference equations with almost periodic coefficients

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1661–1667

For the linear systemof difference equations $x(t + 1) = Ax(t) + P(t)x(t)$, where the matrix $P(t)$ is almost periodic, sufficient conditions are given, which reduce it to a system with a constant matrix.

Article (Ukrainian)

### The existence of a classical solution to the mixed problem for a linear second-order hyperbolic equation

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1232–1238

The paper deals with the problem of solvability of the mixed problem for a linear second-order hyperbolic partial differential equation. The minimal necessary and sufficient conditions for the existence of a unique classical solution to this problem are established.

Article (Ukrainian)

### On the periodic solutions of the second-order wave equations. V

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1115–1121

It is established that the linear problem $u_{tt} - a^2 u_{xx} = g(x, t),\quad u(0, t) = u(\pi, t),\quad u(x, t + T) = u(x, t)$ is always solvable in the space of functions $A = \{g:\; g(x, t) = g(x, t + T) = g(\pi - x, t) = -g(-x, t)\}$ provided that $aTq = (2p - 1)\pi, \quad (2p - 1, q) = 1$, where $p, q$ are integers. To prove this statement, an explicit solution is constructed in the form of an integral operator which is used to prove the existence of a solution to aperiodic boundary value problem for nonlinear second order wave equation. The results obtained can be employed in the study of solutions to nonlinear boundary value problems by asymptotic methods.

Article (Russian)

### On N. N. Bogolyubov's works in classical and quantum statistical mechanics

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 155–201

A review of N. N. Bogolyubov's works in classical and quantum statistical mechanics is presented.

Obituaries (Ukrainian)

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

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

Anniversaries (Ukrainian)

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

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

Article (Ukrainian)

### A class of nonlinear oscillational systems admitting exact solution of the Fokker-Planck-Kolmogorov equation

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1383–1388

Article (Ukrainian)

### Oscillations in first-order systems with lag

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1193–1201

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)

### Approximate symmetry of a nonlinear heat equation

Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 833-837

Anniversaries (Russian)

### Aleksey Nikolaevich Bogolyubov (on his 80th birthday)

Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 864-865

Anniversaries (Russian)

### Samuil Davidovich Eidelman (On his sixtieth birthday)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 578

Article (Ukrainian)

### Some aspects of a gradient holonomic algorithm in the theory of integrability of nonlinear dynamic systems and computer algebra problems

Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 78-81

Article (Ukrainian)

### A two-point problem for systems of hyperbolic equations

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1657–1663

Article (Ukrainian)

### The ideas of Krylov and Bogolyubov in the theory of differential equations and mathematical physics and their development

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 291–302

Brief Communications (Russian)

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

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

Article (Ukrainian)

### Periodic solutions of second-order wave equations. IV

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 757–763

Article (Ukrainian)

### Interaction of random forces on gyroscopic systems

Ukr. Mat. Zh. - 1988. - 40, № 5. - pp. 592-599

Article (Ukrainian)

### Algebraic scheme of discrete approximations of linear and nonlinear dynamical systems of mathematical physics

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 453-458

Article (Ukrainian)

### Asymptotic decomposition of completely integrable pfaffian systems with small parameter

Ukr. Mat. Zh. - 1988. - 40, № 3. - pp. 349-356

Article (Ukrainian)

### Asymptotic and exact solutions of a multidimensional nonlinear equation of the Schrodinger type

Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 744–751

Article (Ukrainian)

### Random oscillations in quasilinear systems of stochastic integrodifferential equations

Ukr. Mat. Zh. - 1987. - 39, № 4. - pp. 472–478

Article (Ukrainian)

### Periodic solutions of second-order wave equations. III

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 347–353

Article (Ukrainian)

### Asymptotic decomposition of differential systems with a small parameter

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 194-204

Article (Ukrainian)

### Periodic solutions of second-order wave equations. II

Ukr. Mat. Zh. - 1986. - 38, № 6. - pp. 733-739

Article (Ukrainian)

### Yurii Dmitrievich Sokolov (on his ninetieth birthday)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 534–538

Article (Ukrainian)

### Periodic solutions of second-order wave equations. I.

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 593–600

Article (Ukrainian)

### Evgeny Yakovlevich Remez (on his ninetieth birthday)

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

Article (Ukrainian)

### Equivalent linearization of systems with distributed parameters

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 464-471

Article (Ukrainian)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 128–131

Article (Ukrainian)

### Integral manifolds, stability, and bifurcation of solutions of singularly perturbed functional-differential equations

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 335–340

Article (Ukrainian)

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 128–131

Article (Ukrainian)

### Random oscillations in quasilinear systems of stochastic differential equations with delay

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 181–187

Article (Ukrainian)

### Lyapunov functions and bounded solutions of linear systems of differential equations

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 39–49

Article (Ukrainian)

### Complete integrability of the differential equations connected with the problem of nonlinear oscillations of a homogeneous beam compressed longitudinally

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 727–729

Article (Ukrainian)

### A control problem for systems, of second-order differential equations with retarded argument

Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 594–599

Article (Ukrainian)

### Solution of a control problem for systems with delay by the method of two-sided approximations

Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 462–467

Article (Ukrainian)

### Random oscillations in some viscoelastic nonlinear systems

Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 468–472

Article (Ukrainian)

### Vladimir Semenovich Korolyuk (on his sixtieth birthday)

Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 488–489

Article (Ukrainian)

### Application of quadratic forms in the theory of invariant manifolds

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 306–316

Article (Ukrainian)

### Yurii Makarovich Berezansky (on his sixtieth birthday)

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 342–343

Article (Ukrainian)

### Differential-difference dynamical systems associated with the Dirac difference operator and their total integrability

Ukr. Mat. Zh. - 1985. - 37, № 2. - pp. 180 – 186

Article (Ukrainian)

### Averaging method in systems with impulses

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

Article (Ukrainian)

### Bounded solutions of nonlinear systems of differential equations

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 720 – 729

Article (Ukrainian)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 547 – 558

Article (Ukrainian)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 584 – 595

Article (Ukrainian)

### Nikolay Nikolayevich Bogolyubov (on his 70th birthday)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 651 – 652

Article (Ukrainian)

### Integrability of ideals in Grassman algebras on differentiable manifolds and some of its applications

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 451 – 456

Article (Ukrainian)

### Asymptotic decomposition of systems of nonlinear ordinary differential equations

Ukr. Mat. Zh. - 1984. - 36, № 1. - pp. 35 - 45

Article (Ukrainian)

Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 448—464

Article (Ukrainian)

### Vladimir Nikolaevich Koshlyakov (on his sixtieth birthday)

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 76

Article (Ukrainian)

### Qualitative investigation of a mathematical model of the thermocline

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 631—633

Article (Ukrainian)

### Sergei Nikolaevich Chernikov (on his sixtieth birthday)

Ukr. Mat. Zh. - 1982. - 34, № 4. - pp. 476—477

Article (Ukrainian)

### Aleksandr Mikhailovich Lyapunov (the 125th anniversary of his birth)

Ukr. Mat. Zh. - 1982. - 34, № 4. - pp. 536—537

Article (Ukrainian)

### Ostap Stepanovich Parasiuk (on his sixtieth birthday)

Ukr. Mat. Zh. - 1981. - 33, № 6. - pp. – C 800-801

Article (Ukrainian)

### Asymptotic solution of a class of boundary-value problems

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 846–853

Article (Ukrainian)

### Work of A. V. Skorokhod on the theory of stochastic processes

Ukr. Mat. Zh. - 1980. - 32, № 4. - pp. 523–527

Article (Ukrainian)

### Galerkin's method in the theory of quasiperiodic solutions of nonlinear differential equations with lag

Ukr. Mat. Zh. - 1980. - 32, № 4. - pp. 553–557

Article (Ukrainian)

### A probabilistic model of the operation of a continuous filter

Ukr. Mat. Zh. - 1980. - 32, № 3. - pp. 361 - 364

Article (Ukrainian)

### Investigations of V. A. Zmorovich in the area of geometric function theory

Ukr. Mat. Zh. - 1979. - 31, № 6. - pp. 756–760

Article (Ukrainian)

### A survey of the main works of N. N. Bogolyubov in mathematics and theoretical physics

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 341–350

Article (Ukrainian)

### Methods for averaging hyperbolic systems with rapid and slow variables mixed problem

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 398–406

Article (Ukrainian)

### Averaging methods for hyperbolic systems with fast and slow variables Cauchy problem

Ukr. Mat. Zh. - 1979. - 31, № 2. - pp. 149–156

Article (Ukrainian)

### Asymptotic expansions in nonlinear mechanics

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

Article (Ukrainian)

### Some problems in the comparison method in nonlinear mechanics

Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 823–829

Article (Ukrainian)

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp.

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)

### Development of oscillation theory of the solutions of differential equations with retarded argument

Ukr. Mat. Zh. - 1977. - 29, № 3. - pp. 313–323

Article (Ukrainian)

### Oscillations of a system with lag depending on the system's state

Ukr. Mat. Zh. - 1977. - 29, № 3. - pp. 398–404

Article (Ukrainian)

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

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

Article (Ukrainian)

### Longitudinal-transversal vibrations of viscoelastic rods with consideration of physical and geometric nonlinearities

Ukr. Mat. Zh. - 1976. - 28, № 5. - pp. 629–638

Article (Ukrainian)

### On asymptotic integration of weakly nonlinear systems

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

Article (Ukrainian)

### Asymptotic method for probability problems

Ukr. Mat. Zh. - 1975. - 27, № 4. - pp. 471–476

Article (Ukrainian)

### Parametrically excited oscillations of a rod subject to a nonlinear law of elasticity

Ukr. Mat. Zh. - 1975. - 27, № 3. - pp. 395–400

Article (Ukrainian)

### The increase in the stability of a flexible circular flat plate by the use of high frequency compressive forces

Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 402–408

Article (Ukrainian)

### Bilateral bounded and almost-periodic solutions of certain systems of differential equations with a deviating argument

Ukr. Mat. Zh. - 1973. - 25, № 6. - pp. 618-629

Article (Ukrainian)

### Periodic solutions of discrete second order difference equations

Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 537—541

Article (Ukrainian)

### Quasi-periodic oscillations in linear systems

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

Article (Ukrainian)

### Averaging of integro-differential and integral equations

Ukr. Mat. Zh. - 1972. - 24, № 1. - pp. 30–48

Article (Ukrainian)

### The second Bogolyubov theorem on the averaging method for differential equations with lagging argument

Ukr. Mat. Zh. - 1972. - 24, № 1. - pp. 49–56

Article (Ukrainian)

### Foundation of the method of averaging for differential-difference equations in Hilbert space

Ukr. Mat. Zh. - 1971. - 23, № 6. - pp. 745–752

Article (Ukrainian)

### A veraging in stochastic systems

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 318–345

Article (Ukrainian)

### Nikolai Ivanovich Muskhelishvili (on his eightieth birthday)

Ukr. Mat. Zh. - 1971. - 23, № 1. - pp. 49–51

Anniversaries (Russian)

### Mikhail Alekseevich Lavrentiev (on his seventieth birthday)

Ukr. Mat. Zh. - 1970. - 22, № 6. - pp. 801-805

Article (Ukrainian)

### On the averaging principle for hyperbolic equations along characteristics

Ukr. Mat. Zh. - 1970. - 22, № 5. - pp. 600—610

Anniversaries (Russian)

### Nikolay Petrovich Sokolov (on his eightieth birthday)

Ukr. Mat. Zh. - 1970. - 22, № 5. - pp. 657-659

Article (Ukrainian)

### Review of reports at the International Conference on Nonlinear Vibrations, Kiev

Ukr. Mat. Zh. - 1970. - 22, № 1. - pp. 132–140

Anniversaries (Russian)

### Nikolai Nikolaevich Bogolyubov (on his sixtieth birthday)

Ukr. Mat. Zh. - 1969. - 21, № 4. - pp. 435–446

Article (Russian)

### Periodic solutions of nonlinear systems of neutral partial differential equations

Ukr. Mat. Zh. - 1969. - 21, № 4. - pp. 475–486

Anniversaries (Russian)

### Aleksei Vasil'evich Pogorelov (on his fiftieth birthday)

Ukr. Mat. Zh. - 1969. - 21, № 3. - pp. 354–360

Article (Ukrainian)

### The principal achievements in mathematics in the Academy of Sciences of the Ukrainian SSR during half a century

Ukr. Mat. Zh. - 1969. - 21, № 2. - pp. 147–164

Article (Russian)

### The development of computational mathematics and mathematical modelling at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR

Ukr. Mat. Zh. - 1969. - 21, № 2. - pp. 165–172

Article (Ukrainian)

### Stable integral manifolds for a class of singularly perturbed systems with lag

Ukr. Mat. Zh. - 1968. - 20, № 6. - pp. 791–801

Article (Ukrainian)

### Reduction principle in the theory of stability of linear differential equations

Ukr. Mat. Zh. - 1968. - 20, № 5. - pp. 654–660

Article (Ukrainian)

### Construction of solutions of almost diagonal systems of linear differential equations using the accelerated convergence method

Ukr. Mat. Zh. - 1968. - 20, № 2. - pp. 166–175

Article (Ukrainian)

### The Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR and the fiftieth anniversary of the Soviet Government

Ukr. Mat. Zh. - 1967. - 19, № 6. - pp. 3–15

Article (Ukrainian)

### The principal investigations of the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR during the years of Soviet power

Ukr. Mat. Zh. - 1967. - 19, № 6. - pp. 16–31

Article (Ukrainian)

### Principal results of research in the mathematical-physics and nonlinear-vibration section of the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR

Ukr. Mat. Zh. - 1967. - 19, № 6. - pp. 39–64

Article (Ukrainian)

### Improved (in the mean) asymptotic representations for essentially nonlinear systems

Ukr. Mat. Zh. - 1967. - 19, № 5. - pp. 76–86

Article (Ukrainian)

### Pavel Feodosevich Filchakov (on his fiftieth birthday)

Ukr. Mat. Zh. - 1966. - 18, № 6. - pp. 97-101

Anniversaries (Russian)

### Yurij Dmitrievich Sokolov (on his sixtieth birthday)

Ukr. Mat. Zh. - 1966. - 18, № 4. - pp. 94-101

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)

### On the integral manifold of a nonlinear system in a Hilbert space

Ukr. Mat. Zh. - 1965. - 17, № 5. - pp. 43-53

Letter (Russian)

### Remarks on the article «On construction of the general solution of nonlinear differential equations by a method securing «accelerated convergence» (Ukr. Math. J., vol. XVI, No. 4)

Ukr. Mat. Zh. - 1964. - 16, № 5. - pp. 712

Article (Russian)

### On the construction of a general solution of nonlinear differential equations by means of a method securing «accelerated» convergence

Ukr. Mat. Zh. - 1964. - 16, № 4. - pp. 475-501

Article (Russian)

### On the investigation of a integral manifold for a system of nonlinear equations, close to equations with variable coefficients, in a Hilbert space

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 334-338

The author considers a system of differential equations $$\frac{d\varphi}{dt} = \omega(t) + P(t, \varphi, h, \varepsilon)$$ $$\frac{dh}{dt} = H(t)h + Q(t, \varphi, h, \varepsilon)$$ where $h$ and $Q$ are vector functions with values in Hilbert space $H$, $\omega(t)$ is a limited operator function in Hilbert space $H$, for which the real parts of all points of the spectrum are negative. The existence and stability of a one-dimensional integral manifold for system (1) is proved with certain assumptions.

Article (Russian)

### On an integral manifold of nonlinear differential equations containing slow and fast motions

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 157-163

The authors establish the existence and properties of an $s + 1$ -dimensional local integral manifold of a system of $l + m + n$ nonlinear differential equations of the form $$\frac{dx}{dt} = X(y,z)x + \varepsilon X_1(t, x, y, z),$$ $$\frac{dy}{dt} =Y(x, z), y + \varepsilon Y_1 (t, x, y, z),$$ $$\frac{dz}{dt} = \varepsilon Z_1 (t, x, y, z),$$ where $x, y$ characterize the fast, and $z$ the slow motions.

Chronicles (Russian)

### Second conference on nonlinear oscillations of the Polish and Czechoslovakian Academies of Sciences

Ukr. Mat. Zh. - 1963. - 15, № 1. - pp. 115-116

BookReview (Russian)

### G. S. Pisarenko, Energy Dissipation of Mechanical Vibrations

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 456-457

Chronicles (Russian)

### International symposium on nonlinear vibrations

Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 115-116

BookReview (Russian)

### S. Z. Stokalo, Operational methods and their development in the theory of linear differential equations with variable coefficients

Ukr. Mat. Zh. - 1961. - 13, № 3. - pp. 116-117

Article (Russian)

### On Periodic Solutions of Systems of Nonlinear Equations with a Small Parameter

Ukr. Mat. Zh. - 1960. - 12, № 4. - pp. 391 - 401

The authors consider a system of nonlinear differential equations containing a small parameter with undifferentiated right parts of types (1) and (37). Making some assumptions, the existence unique and asymptotic stability of a periodic solution is proved for such systems, and an estimate is found for the difference between the exact solution of the systems under consideration and their first approximation, which can be found without any essential difficulty.

Anniversaries (Russian)

### Mikhail Alexeyevich Lavrentyev (on his sixtieth birthday)

Ukr. Mat. Zh. - 1960. - 12, № 4. - pp. 490 - 491

BookReview (Russian)

### Linear Differential Equations with Variable Coefficients (asymptotic methods and criteria of stability and instability of solutions)

Ukr. Mat. Zh. - 1960. - 12, № 4. - pp. 492 - 493

Anniversaries (Russian)

### Nikolai Mitrofanovich Krylov (on the 80tn anniversary of his birth)

Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 205 - 208