2017
Том 69
№ 9

All Issues

Mitropolskiy Yu. A.

Articles: 148
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

Anniversaries (Ukrainian)

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

Berezansky Yu. M., Dorogovtsev A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Perestyuk N. A., Rebenko A. L., Ronto A. M., Ronto M. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M.

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

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.

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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.

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

Anniversaries (Russian)

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

Martynyuk A. A., Mitropolskiy Yu. A.

Full text (.pdf)

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

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.

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

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.

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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.

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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.

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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

Khoma-Mohyl's'ka S. H., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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

Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

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)

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.

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

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.

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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.

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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

Kolomiets O. V., Kolomiyets V. G., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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)

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

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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.

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

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.

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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.

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

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

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.

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

Anniversaries (Russian)

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

Khruslov E. Ya., Marchenko V. O., Mitropolskiy Yu. A., Pogorelov A. V., Samoilenko A. M., Skrypnik I. V.

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

Article (Ukrainian)

Oleksii Mykolajovych Boholyubov (on His 90th Birthday)

Koshlyakov V. N., Mitropolskiy Yu. A., Samoilenko A. M., Urbansky V. M.

Full text (.pdf)

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

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.

Article (Ukrainian)

Problems with free boundaries for nonlinear parabolic equations

Berezovs'kyi M. A., Berezovsky A. A., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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

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

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

Article (Ukrainian)

A periodic problem for the inhomogeneous equation of string oscillations

Khoma G. P., Mitropolskiy Yu. A., Tsynalko P. V.

↓ Abstract   |   Full text (.pdf)

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

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

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

Article (Russian)

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

Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

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

Berezovsky A. A., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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.

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)

Bogolyubov averaging and normalization procedures in nonlinear mechanics. I

Lopatin A. K., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

Asymptotic methods in the theory of nonlinear random oscillations

Kolomiyets V. G., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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

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)

Asymptotic behavior of a class of stochastic semigroups in the Bernoulli scheme

Mitropolskiy Yu. A.

Full text (.pdf)

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

Article (Ukrainian)

Reducibility of linear systems of difference equations with almost periodic coefficients

Martynyuk D. I., Mitropolskiy Yu. A., Tynnyi V. I.

↓ Abstract   |   Full text (.pdf)

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

We establish sufficient conditions of the reducibility of the linear system of difference equationsx(t+1)=Ax(t) + P(t) x(t) with an almost periodic matrixP(t) to a system with a constant matrix.

Article (Ukrainian)

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

Khoma G. P., Mitropolskiy Yu. A.

Full text (.pdf)

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

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)

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

Mitropolskiy Yu. A., Nguyen Tien Khiem

Full text (.pdf)

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

Article (Ukrainian)

Oscillations in first-order systems with lag

Mitropolskiy Yu. A., Nguyen Dong An, Nguyen Tien Khiem

Full text (.pdf)

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

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)

Approximate symmetry of a nonlinear heat equation

Mitropolskiy Yu. A., Shul'ga M. V.

Full text (.pdf)

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

Anniversaries (Russian)

Aleksey Nikolaevich Bogolyubov (on his 80th birthday)

Kolomiyets V. G., Mitropolskiy Yu. A.

Full text (.pdf)

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

Anniversaries (Russian)

Samuil Davidovich Eidelman (On his sixtieth birthday)

Berezansky Yu. M., Gorbachuk M. L., Ivasyshen S. D., Korolyuk V. S., Mitropolskiy Yu. A., Skrypnik I. V.

Full text (.pdf)

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

Fil' B. N., Mitropolskiy Yu. A., Prikarpatskii A. K.

Full text (.pdf)

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

Article (Ukrainian)

A two-point problem for systems of hyperbolic equations

Mitropolskiy Yu. A., Urmancheva L. B.

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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

Mitropolskiy Yu. A.

Full text (.pdf)

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

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)

Periodic solutions of second-order wave equations. IV

Khoma G. P., Mitropolskiy Yu. A.

Full text (.pdf)

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

Article (Ukrainian)

Interaction of random forces on gyroscopic systems

Mitropolskiy Yu. A., Nosirov F. U.

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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

Mitropolskiy Yu. A., Prikarpatskii A. K., Samoilenko V. G.

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

Article (Ukrainian)

Asymptotic decomposition of completely integrable pfaffian systems with small parameter

Lopatin A. K., Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Mitropolskiy Yu. A., Shul'ga M. V.

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

Article (Ukrainian)

Random oscillations in quasilinear systems of stochastic integrodifferential equations

Mitropolskiy Yu. A., Nguyen Dong An

Full text (.pdf)

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

Article (Ukrainian)

Periodic solutions of second-order wave equations. III

Khoma G. P., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Asymptotic decomposition of differential systems with a small parameter

Lopatin A. K., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Periodic solutions of second-order wave equations. II

Khoma G. P., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Yurii Dmitrievich Sokolov (on his ninetieth birthday)

Luchka A. Y., Mitropolskiy Yu. A., Shevelo V. N.

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

Article (Ukrainian)

Periodic solutions of second-order wave equations. I.

Khoma G. P., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Evgeny Yakovlevich Remez (on his ninetieth birthday)

Dzyadyk V. K., Gavrilyuk V. T., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Equivalent linearization of systems with distributed parameters

Berezovsky A. A., Konovalova N. R., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Galitsyn A. S., Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Fodchuk V. I., Klevchuk I. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Dobrovol'skii V. A., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Random oscillations in quasilinear systems of stochastic differential equations with delay

Mitropolskiy Yu. A., Nguyen Dong An

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

Article (Ukrainian)

Lyapunov functions and bounded solutions of linear systems of differential equations

Kulik V. L., Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A., Prikarpatskii A. K., Samoilenko V. G.

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

Article (Ukrainian)

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

Martynyuk D. I., Mitropolskiy Yu. A., Yurchik A. I.

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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

Martynyuk D. I., Mitropolskiy Yu. A., Yurchik A. I.

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

Article (Ukrainian)

Random oscillations in some viscoelastic nonlinear systems

Mitropolskiy Yu. A., Nguyen Dong An

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

Article (Ukrainian)

Vladimir Semenovich Korolyuk (on his sixtieth birthday)

Gusak D. V., Mitropolskiy Yu. A., Skorokhod A. V.

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

Article (Ukrainian)

Application of quadratic forms in the theory of invariant manifolds

Kulik V. L., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Yurii Makarovich Berezansky (on his sixtieth birthday)

Gorbachuk V. I., Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A., Samoilenko V. G.

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

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)

Bounded solutions of nonlinear systems of differential equations

Kulik V. L., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Mitropolskiy Yu. A., Strok V. V.

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

Article (Ukrainian)

Mitropolskiy Yu. A.

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

Article (Ukrainian)

Nikolay Nikolayevich Bogolyubov (on his 70th birthday)

Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A., Prikarpatskii A. K., Samoilenko V. G.

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

Article (Ukrainian)

Asymptotic decomposition of systems of nonlinear ordinary differential equations

Lopatin A. K., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Kalinovich V. N., Koshlyakov V. N., Mitropolskiy Yu. A., Storozhenko V. A., Temchenko M. Ye.

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

Article (Ukrainian)

Vladimir Nikolaevich Koshlyakov (on his sixtieth birthday)

Lukovsky I. O., Mitropolskiy Yu. A., Onishchenko S. M.

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

Article (Ukrainian)

Qualitative investigation of a mathematical model of the thermocline

Berezovsky A. A., Boguslavsky A. S., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Sergei Nikolaevich Chernikov (on his sixtieth birthday)

Bogolyubov A. N., Mitropolskiy Yu. A., Zaitsev D. I.

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

Article (Ukrainian)

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

Martynyuk A. A., Mitropolskiy Yu. A., Zubov V. I.

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

Article (Ukrainian)

Ostap Stepanovich Parasiuk (on his sixtieth birthday)

Bogoliubov N. N., Fushchich V. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Asymptotic solution of a class of boundary-value problems

Krivosheya S. A., Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Korolyuk V. S., Kovalenko I. N., Mikhalevich V. S., Mitropolskiy Yu. A.

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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

Martynjuk, Martynyuk D. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

A probabilistic model of the operation of a continuous filter

Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Gudz L. A., Mitropolskiy Yu. A., Tamrazov P. M.

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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

Mitropolskiy Yu. A., Parasyuk O. S., VIadimirov V. S.

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

Article (Ukrainian)

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

Khoma G. P., Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Khoma G. P., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Asymptotic expansions in nonlinear mechanics

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Ukrainian)

Some problems in the comparison method in nonlinear mechanics

Martynyuk A. A., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Korolyuk V. S., Mitropolskiy Yu. A., Shevelo V. N.

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

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.

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

Article (Ukrainian)

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

Mitropolskiy Yu. A., Shevelo V. N.

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

Article (Ukrainian)

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

Mitropolskiy Yu. A., Nguyen Kkhak Lan

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

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)

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

Berezovsky A. A., Kurbanov I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

On asymptotic integration of weakly nonlinear systems

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Ukrainian)

Asymptotic method for probability problems

Gusak D. V., Mitropolskiy Yu. A., Skorokhod A. V., Turbin A. F.

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

Article (Ukrainian)

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

Berezovsky A. A., Mitropolskiy Yu. A., Turgunov N.

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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

Berezovsky A. A., Mitropolskiy Yu. A., Turgunov N.

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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

Boichuk O. F., Kalinovich V. N., Koshlyakov V. N., Mitropolskiy Yu. A., Storozhenko V. A., Temchenko M. E.

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

Article (Ukrainian)

Periodic solutions of discrete second order difference equations

Mikhailovskaya N. A., Mitropolskiy Yu. A.

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

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 of integro-differential and integral equations

Filatov A. N., Mitropolskiy Yu. A.

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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

Fodchuk V. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Fodchuk V. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

A veraging in stochastic systems

Kolomiyets V. G., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Nikolai Ivanovich Muskhelishvili (on his eightieth birthday)

Mitropolskiy Yu. A., Shevelo V. N.

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

Anniversaries (Russian)

Mikhail Alekseevich Lavrentiev (on his seventieth birthday)

Editorial Board, Mitropolskiy Yu. A., Shtokalo I. Z.

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

Article (Ukrainian)

On the averaging principle for hyperbolic equations along characteristics

Khoma G. P., Mitropolskiy Yu. A.

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

Anniversaries (Russian)

Nikolay Petrovich Sokolov (on his eightieth birthday)

Chernikov S. N., Mitropolskiy Yu. A., Sokolov Yu. D., Velmin V. P.

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

Article (Ukrainian)

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

Mitropolskiy Yu. A., Shevelo V. N.

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

Anniversaries (Russian)

Nikolai Nikolaevich Bogolyubov (on his sixtieth birthday)

Mitropolskiy Yu. A., Parasyuk O. S., Shelest V. P.

Full text (.pdf)

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

Article (Russian)

Periodic solutions of nonlinear systems of neutral partial differential equations

Mitropolskiy Yu. A., Tkach B. P.

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

Anniversaries (Russian)

Aleksei Vasil'evich Pogorelov (on his fiftieth birthday)

Akhiezer N. I., Blank J.P., Marchenko V. O., Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A.

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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

Fil'chakov F. P., Mitropolskiy Yu. A., Panchishin V. I.

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

Article (Ukrainian)

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

Fodchuk V. I., Mitropolskiy Yu. A.

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

Article (Ukrainian)

Reduction principle in the theory of stability of linear differential equations

Belan E. P., Mitropolskiy Yu. A.

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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

Belan E. P., Mitropolskiy Yu. A.

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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

Breus K. A., Mitropolskiy Yu. A.

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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

Breus K. A., Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A.

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

Article (Ukrainian)

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

Mitropolskiy Yu. A., Senik P. M.

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

Article (Ukrainian)

Pavel Feodosevich Filchakov (on his fiftieth birthday)

Lavrik V. I., Mitropolskiy Yu. A., Sokolov Yu. D.

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

Anniversaries (Russian)

Yurij Dmitrievich Sokolov (on his sixtieth birthday)

Kurpel N. S., Luchka A. Y., Mitropolskiy Yu. A., Shevelo V. N.

Full text (.pdf)

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

Mitropolskiy Yu. A., Samoilenko A. M.

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

Article (Russian)

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

Lykova O. B., Mitropolskiy Yu. A.

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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)

Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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

Lykova O. B., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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

Mitropolskiy Yu. A.

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

BookReview (Russian)

G. S. Pisarenko, Energy Dissipation of Mechanical Vibrations

Mitropolskiy Yu. A.

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

Chronicles (Russian)

International symposium on nonlinear vibrations

Mitropolskiy Yu. A.

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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

Mitropolskiy Yu. A., Parasyuk O. S., Sokolov Yu. D.

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

Article (Russian)

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

Lykova O. B., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

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)

Fil'chakov F. P., Mitropolskiy Yu. A., Shtokalo I. Z.

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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)

Mitropolskiy Yu. A., Shtokalo I. Z.

Full text (.pdf)

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

Anniversaries (Russian)

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

Bogoliubov N. N., Mitropolskiy Yu. A.

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