2017
Том 69
№ 9

All Issues

Samoilenko A. M.

Articles: 146
Article (Ukrainian)

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

Samoilenko A. M.

↓ Abstract

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)

Romanyuk A. S., Romanyuk V. S., Samoilenko A. M., Savchuk V. V., Serdyuk A. S., Sokolenko I. V.

Full text (.pdf)

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)

Berezansky Yu. M., Boichuk A. A., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Parasyuk I. O., Perestyuk N. A., Samoilenko A. M., Sharkovsky O. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Volodymyr Leonidovych Makarov (on his 75th birthday)

Korolyuk V. S., Lukovsky I. O., Nesterenko B. B., Nikitin A. G., Perestyuk N. A., Samoilenko A. M., Solodkii S. G., Trohimchuk Yu. Yu

Full text (.pdf)

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

Anniversaries (Ukrainian)

Mykola Oleksiiovych Perestyuk (on his 70th birthday)

Boichuk A. A., Gorbachuk M. L., Gorodnii M. F., Khruslov E. Ya., Lukovsky I. O., Makarov V. L., Parasyuk I. O., Samoilenko A. M., Samoilenko V. G., Sharkovsky O. M., Shevchuk I. A., Slyusarchuk V. Yu., Stanzhitskii A. N.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Volodymyr Semenovych Korolyuk (on his 90th birthday)

Bratiichuk N. S., Gusak D. V., Kovalenko I. N., Lukovsky I. O., Makarov V. L., Samoilenko A. M., Samoilenko I. V.

Full text (.pdf)

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

Article (Ukrainian)

Dynamical Bifurcation of Multifrequency Oscillations in a Fast-Slow System

Parasyuk I. O., Repeta B. V., Samoilenko A. M.

↓ Abstract

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)

Babenko V. F., Davydov O. V., Kofanov V. A., Parfinovych N. V., Pas'ko A. N., Romanyuk A. S., Ruban V. I., Samoilenko A. M., Shevchuk I. A., Shumeiko A. A., Timan M. P., Trigub R. M., Vakarchuk S. B., Velikin V. L.

Full text (.pdf)

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

Article (Russian)

Differential Equations with Bistable Nonlinearity

Nizhnik L. P., Samoilenko A. M.

↓ Abstract

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

Lukovsky I. O., Samoilenko A. M., Storozhenko V. A.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Yurii Stephanovych Samoilenko (on his 70th birthday)

Berezansky Yu. M., Boichuk A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Nizhnik L. P., Samoilenko A. M., Sharko V. V., Sharkovsky O. M., Trohimchuk Yu. Yu

Full text (.pdf)

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

Anniversaries (Ukrainian)

Major Pylypovych Timan (on his 90th birthday)

Babenko V. F., Motornyi V. P., Peleshenko B. I., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Trigub R. M., Vakarchuk S. B.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Berezansky Yu. M., Gerasimenko V. I., Khruslov E. Ya., Kochubei A. N., Mikhailets V. A., Nizhnik L. P., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

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

Article (Russian)

Dynamics of periodic modes for the phenomenological equation of spin combustion

Belan E. P., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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)

Korolyuk V. S., Lukovsky I. O., Perestyuk N. A., Pratsiovytyi M. V., Samoilenko A. M., Yakovets V. P.

Full text (.pdf)

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)

Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Sokolenko I. V.

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

Anniversaries (Ukrainian)

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

Gorbachuk M. L., Lukovsky I. O., Makarov V. L., Motornyi V. P., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Sharko V. V., Zaderei P. V.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Danilov V. Ya., Gorodnii M. F., Kirichenko V. V., Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Bakhtin A. K., Gerasimenko V. I., Plaksa S. A., Samoilenko A. M., Sharko V. V., Trohimchuk Yu. Yu, Yacenko V. O., Zelinskii Yu. B.

Full text (.pdf)

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

Article (Ukrainian)

Lipschitzian invariant tori of indefinite monotone system

Lagoda V. A., Parasyuk I. O., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Novak I. H., Samoilenko A. M., Stanzhitskii A. N.

↓ Abstract   |   Full text (.pdf)

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)

Korolyuk V. S., Lukovsky I. O., Samoilenko A. M.

Full text (.pdf)

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

Obituaries (Ukrainian)

Anatolii Volodymyrovych Skorokhod

Korolyuk V. S., Portenko N. I., Samoilenko A. M.

Full text (.pdf)

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

Article (English)

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

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Evtukhov V. M., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M., Vlasenko L. A.

↓ Abstract   |   Full text (.pdf)

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)

Samoilenko A. M.

Full text (.pdf)

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)

Romanyuk A. S., Samoilenko A. M.

Full text (.pdf)

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

Article (Russian)

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

Rutkas A. G., Samoilenko A. M., Vlasenko L. A.

↓ Abstract   |   Full text (.pdf)

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)

Berezansky Yu. M., Bojarski B., Gorbachuk M. L., Kopilov A. P., Korolyuk V. S., Lukovsky I. O., Mitropolskiy Yu. A., Portenko N. I., Reshetnyak Yu. G., Samoilenko A. M., Sharko V. V., Shevchuk I. A., Skorokhod A. V., Tamrazov P. M., Zelinskii Yu. B.

Full text (.pdf)

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

Article (Ukrainian)

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

Adamyan V. M., Berezansky Yu. M., Khruslov E. Ya., Kochubei A. N., Kuzhel' S. A., Marchenko V. O., Mikhailets V. A., Nizhnik L. P., Ptashnik B. I., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Leonіd Andrіyovich Pastur (on his 70th birthday)

Baryakhtar V. G., Berezansky Yu. M., Khruslov E. Ya., Korolyuk V. S., Marchenko V. O., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

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

Obituaries (Ukrainian)

Alexander Ivanovich Stepanets

Gorbachuk M. L., Lukovsky I. O., Mitropolskiy Yu. A., Romanyuk A. S., Rukasov V. I., Samoilenko A. M., Serdyuk A. S., Shevchuk I. A., Zaderei P. V.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Mark Grigorievich Krein (to the centenary of his birth)

Adamyan V. M., Arov D. Z., Berezansky Yu. M., Gorbachuk M. L., Gorbachuk V. I., Mikhailets V. A., Samoilenko A. M.

Full text (.pdf)

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

Denysenko N. L., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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)

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Marchenko V. O., Mitropolskiy Yu. A., Nizhnik L. P., Pastur L. A., Samoilenko A. M., Sharko V. V.

Full text (.pdf)

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

Danylyuk I. M., Petryshyn R. I., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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"

Samoilenko A. M., Savchuk V. V., Sokolenko I. V., Stepanets O. I.

Full text (.pdf)

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

Anniversaries (Ukrainian)

On the 90th birthday of Yurii Alekseevich Mitropol’skii

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Koshlyakov V. N., Lukovsky I. O., Makarov V. L., Perestyuk N. A., Samoilenko A. M., Samoilenko Yu. I., Sharko V. V., Sharkovsky O. M., Stepanets O. I., Tamrazov P. M., Trohimchuk Yu. Yu

Full text (.pdf)

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

Article (Ukrainian)

Some results of the local theory of smooth functions

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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)

Gorbachuk M. L., Lyantse V. É., Markovskii A. I., Mikhailets V. A., Samoilenko A. M.

Full text (.pdf)

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

Obituaries (Ukrainian)

Andrei Reuter (1937-2006)

Bondarenko V. M., Drozd Yu. A., Kirichenko V. V., Mitropolskiy Yu. A., Samoilenko A. M., Samoilenko Yu. S., Sharko V. V., Stepanets O. I.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Olexiy Bogolyubov (03.25.1911 - 01.11.2004)

Dobrovol'skii V. A., Lykova O. B., Mitropolskiy Yu. A., Pustovoytov M. O., Samoilenko A. M., Urbansky V. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Nikolai Perestyuk (60th birthday)

Mitropolskiy Yu. A., Parasyuk I. O., Samoilenko A. M., ShkiI N. I.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Korenovskii A. A., Korolyuk V. S., Koshlyakov V. N., Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Bratiichuk N. S., Gusak D. V., Kovalenko I. N., Portenko N. I., Samoilenko A. M., Skorokhod A. V.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Korolyuk V. S., Portenko N. I., Samoilenko A. M., Sytaya G. N.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

Berezansky Yu. M., Gorbachuk M. L., Gorbachuk V. I., Khruslov E. Ya., Kostyuchenko A. G., Kuzhel' S. A., Marchenko V. O., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

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

Article (Russian)

Conditions for Synchronization of One Oscillation System

Recke L., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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)

Gorbachuk M. L., Gorbachuk V. I., Kondratiev Yu. G., Kostyuchenko A. G., Marchenko V. O., Mitropolskiy Yu. A., Nizhnik L. P., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

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

Announcement (Ukrainian)

The Skorobogat'ko international mathematical conference

Ptashnik B. I., Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Mel'nik V. S., Mel'nyk O. M., Samoilenko A. M.

Full text (.pdf)

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

Chronicles (Ukrainian)

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

Samoilenko A. M., Shevchuk I. A., Stepanets O. I.

Full text (.pdf)

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

Chronicles (Ukrainian)

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

Pritula N. N., Samoilenko A. M.

Full text (.pdf)

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

Nedokis V. A., Samoilenko A. M., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Dudnytskyi P. M., Petryshyn R. I., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Buldygin V. V., Gorodnii M. F., Gusak D. V., Korolyuk V. S., Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Glushchenko A. A., Lyashko I. I., Mitropolskiy Yu. A., Parasyuk I. O., Samoilenko A. M., Samoilenko V. G.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Dmytro Yakovych Petryna (on his 70 th birthday)

Gorbachuk M. L., Khruslov E. Ya., Lukovsky I. O., Marchenko V. O., Mitropolskiy Yu. A., Pastur L. A., Samoilenko A. M., Skrypnik I. V.

Full text (.pdf)

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

Article (English)

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

Blackmore D. L., Prikarpatskii A. K., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Prikarpatskii Ya. A., Samoilenko A. M., Samoilenko V. G.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Petryshyn R. I., Samoilenko A. M., Sopronyuk Т. M.

↓ Abstract   |   Full text (.pdf)

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

Lakusta L. M., Petryshyn R. I., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Prikarpatskii A. K., Samoilenko A. M., Samoilenko V. G.

↓ Abstract   |   Full text (.pdf)

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)

Lukovsky I. O., Mitropolskiy Yu. A., Polozhii G. N., Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Mykola Ivanovych Shkil' (On His 70th Birthday)

Berezansky Yu. M., Korolyuk V. S., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V.

Full text (.pdf)

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

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Boichuk A. A., Boichuk An. A., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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)

Konet I. M., Perestyuk N. A., Samoilenko A. M., Teplinsky Yu. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Lakusta L. M., Petryshyn R. I., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Kaplun Yu. I., Samoilenko A. M., Samoilenko V. G.

↓ Abstract   |   Full text (.pdf)

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)

Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Romanyuk A. S., Romanyuk V. S., Rukasov V. I., Samoilenko A. M., Serdyuk A. S., Shevchuk I. A., Zaderei P. V.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Mykhailo Iosypovych Yadrenko (On His 70th Birthday)

Buldygin V. V., Korolyuk V. S., Kozachenko Yu. V., Mitropolskiy Yu. A., Perestyuk N. A., Portenko N. I., Samoilenko A. M., Skorokhod A. V.

Full text (.pdf)

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

Article (Russian)

On Invariant Tori of Itô Stochastic Systems

Samoilenko A. M., Stanzhitskii A. N.

↓ Abstract   |   Full text (.pdf)

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"

Ptashnik B. I., Samoilenko A. M.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Danilov V. Ya., Mitropolskiy Yu. A., Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M., Stepanenko N. V.

↓ Abstract   |   Full text (.pdf)

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)

Dorogovtsev A. A., Kopytko B.I., Korolyuk V. S., Mitropolskiy Yu. A., Samoilenko A. M., Skorokhod A. V., Sytaya G. N.

Full text (.pdf)

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

Article (Ukrainian)

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

Prikarpatskii Ya. A., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

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

Samoilenko A. M., Samoilenko V. G., Sidorenko Yu. M.

↓ Abstract   |   Full text (.pdf)

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)

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

Samoilenko A. M., Slyusarchuk V. E., Slyusarchuk V. V.

↓ Abstract   |   Full text (.pdf)

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

Kalinovich V. N., Mitropolskiy Yu. A., Onishchenko S. M., Polishchuk A. N., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Gorbachuk M. L., Luchka A. Y., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

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

Chronicles (Ukrainian)

Seminar-School “Mathematical Simulation”

Berezovsky A. A., Khomchenko A. N., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Boundary-value problems with parameters for a multifrequency oscillation system

Petryshyn Ya. R., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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"

Berezovsky A. A., Konet I. M., Lenyuk M. P., Samoilenko A. M., Teplinsky Yu. V.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Yurii L’vovich Daletskii

Berezansky Yu. M., Korolyuk V. S., Krein S. G., Mitropolskiy Yu. A., Samoilenko A. M., Skorokhod A. V.

Full text (.pdf)

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

Article (Russian)

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

Boichuk A. A., Samoilenko A. M., Zhuravlev V. F.

↓ Abstract   |   Full text (.pdf)

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

Kolomiyets V. G., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Parasyuk I. O., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

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

Mitropolskiy Yu. A., Samoilenko A. M., Strok V. V.

↓ Abstract   |   Full text (.pdf)

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)

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

Bazhura B. P., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Martynyuk D. I., Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

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

Brief Communications (Ukrainian)

To the memory of Valentin Anatol'evich Zmorovich

Baranovskii F. T., Berezansky Yu. M., Buldygin V. V., Daletskii Yu. L., Dobrovol'skii V. A., Dzyadyk V. K., Lozovik V. G., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V., Tamrazov P. M., Yaremchuk F. P.

Full text (.pdf)

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

Article (Ukrainian)

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

Pelyukh G. P., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

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

Martynyuk D. I., Perestyuk N. A., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

We establish sufficient conditions for a nonlinear system of difference equations x(t + 1) =x(t) + ? + P(x(t),t)+ ? to be reducible to the system y(t + 1) =y(t) + ?. Here, P(x, t) is a function 2?-periodic in xi(i = 1, ...,n) and almost periodic int with a frequency basis ?.

Article (Ukrainian)

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

Prikarpatskii A. K., Samoilenko A. M., Timchishin O. Ya.

Full text (.pdf)

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

Article (Ukrainian)

On decomposability of countable systems of differential equations

Samoilenko A. M., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

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

Samoilenko A. M., Trofimchuk S. I.

Full text (.pdf)

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

Anniversaries (Ukrainian)

Parasyuk Ostap Stepanovich (his 70th birthday)

Bogoliubov N. N., Fushchich V. I., Mitropolskiy Yu. A., Petrina D. Ya., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

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

Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Unbounded functions with almost periodic differences

Samoilenko A. M., Trofimchuk S. I.

Full text (.pdf)

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

Martynyuk S. V., Samoilenko A. M.

Full text (.pdf)

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

Brief Communications (Russian)

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

Bogolyubov A. N., Charin V. S., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Generalized solutions of impulse systems and the phenomenon of pulsations

Perestyuk N. A., Samoilenko A. M., Trofimchuk S. I.

Full text (.pdf)

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

Article (Ukrainian)

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

Samoilenko A. M.

Full text (.pdf)

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

Mustafaev Kh. Z., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Reducibility of a system of linear differential equations with quasiperiodic coefficients

Samoilenko A. M.

Full text (.pdf)

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

Brief Communications (Russian)

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

Mitropolskiy Yu. A., Parasyuk O. S., Petrina D. Ya., Samoilenko A. M., VIadimirov V. S.

Full text (.pdf)

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

Article (Ukrainian)

Method of averaging in multifrequency systems with slowly varying parameters

Petryshyn R. I., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

The infinite-dimensional Schrodinger operator and its potential perturbations

Samoilenko A. M.

Full text (.pdf)

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

Lykova O. B., Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Stability of certain two-particle systems

Petryshyn R. I., Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M., Svishchuk M. Ya.

Full text (.pdf)

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

Article (Ukrainian)

Averaging method in systems with impulses

Mitropolskiy Yu. A., Perestyuk N. A., Samoilenko A. M.

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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

Kenzhebaev K. K., Laptinskii V. N., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Decomposability of linearized systems of differential equations

Kulik V. L., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Periodic and almost-periodic solutions of impulsive differential equations

Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

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

Ronto V. A., Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M.

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

Article (Ukrainian)

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

Le Lyong Tay, Samoilenko A. M.

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

Article (Ukrainian)

Asymptotic expansions in nonlinear mechanics

Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Continuity of Green's function for the invariant torus problem

Kulik V. L., Samoilenko A. M.

Full text (.pdf)

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

Mitropolskiy Yu. A., Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

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

Dvorak A. V., Samoilenko A. M.

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

Article (Ukrainian)

Multifrequency oscillations of weakly nonlinear second-order systems

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Ukrainian)

On asymptotic integration of weakly nonlinear systems

Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

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

Article (Ukrainian)

Kulik V. L., Samoilenko A. M.

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

Article (Ukrainian)

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

Kulik V. L., Samoilenko A. M.

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

Article (Ukrainian)

Existence of invariant manifolds of systems with delay

Martynyuk D. I., Samoilenko A. M.

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

Article (Ukrainian)

The method of averaging in systems with an impulsive action

Perestyuk N. A., Samoilenko A. M.

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

Article (Ukrainian)

Invariant sets of systems with instantaneous changes in standard form

Perestyuk N. A., Samoilenko A. M.

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

Article (Ukrainian)

Projection method for equations with nonpotential operators

Samoilenko A. M.

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

Article (Ukrainian)

Quasi-periodic oscillations in linear systems

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Ukrainian)

Averaging method for investigating systems subjected to an impulsive action

Samoilenko A. M.

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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

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Russian)

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

Samoilenko A. M.

Full text (.pdf)

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

Brief Communications (Russian)

On periodic solutions of differential equations with undifferentiable right parts

Samoilenko A. M.

Full text (.pdf)

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

Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M.

Full text (.pdf)

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