yurii alekseevich mitropol’skii (a tribute in honor of his ninetieth birthday)

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 1, pp. 1–9. c© Pleiades Publishing, Ltd., 2007.Original Russian Text c© the Editorial Board, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 1, pp. 3–10.

MEMBERS OF SCIENTIFIC COMMUNITY

Yurii Alekseevich Mitropol’skii(A Tribute in Honor of His Ninetieth Birthday)

DOI: 10.1134/S0012266107010016

On January 3, Yurii Alekseevich Mitropol’skii, Academician of the National Academy of Sciencesof Ukraine and the Russian Academy of Sciences, celebrated his ninetieth birthday.

Yurii Alekseevich Mitropol’skii was born on January 3, 1917 in the village of Chernyshovka,Poltava province. His father, Aleksei Savvich Mitropol’skii, attended St. Petersburg University;he went to the front in 1914 and participated in military operations until the war ended. In 1919,Mitropol’skii’s family moved to Kiev. In 1938, Yurii Alekseevich Mitropol’skii entered the Physical-Mathematical Faculty of Kiev University. From 1943 until the end of the Great Patriotic war, he wasat the front as commander of an artillery reconnaissance platoon.

For service in battle, he was decorated with two Orders of the Red Star, Order of the PatrioticWar (Degree II), and medals.

After demobilization in 1946, Mitropol’skii worked as a junior researcher in the Departmentof Nonlinear Mechanics at the Institute of Structural Mechanics of the Academy of Sciences ofthe Ukrainian Republic. Here, under the supervision by N.N. Bogolyubov, he began his scien-tific activity. His first scientific results dealt with the investigation of resonances in nonlinearoscillation systems with slow parameters on the basis of Krylov–Bogolyubov asymptotic methods.Mitropol’skii defended his Philosophy Doctor thesis on this topic in 1948 and the Doctor of Sciencesthesis “Slow Processes in Nonlinear Oscillation Systems with Many Degrees of Freedom” in 1951.

Since 1950, Mitropol’skii has been working at the Institute of Mathematics of the Academy ofSciences of the Ukrainian Republic (now the National Academy of Sciences of Ukraine). In 1949–89,he simultaneously read special courses on ordinary differential equations including stability theoryand theory of oscillations at the Mechanical-Mathematical Faculty of Kiev University. In 1953–2001, Mitropol’skii headed the Department of Mathematical Physics and Theory of NonlinearOscillations.

He was Director of the Institute of Mathematics of the Academy of Sciences of the UkrainianRepublic in 1958–87 and was elected Honorary Director of the institute in 1987.

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2 YURII ALEKSEEVICH MITROPOL’SKII

Mitropol’skii was elected Corresponding Member of the Academy of Sciences of the UkrainianRepublic in 1958, Academician of the Academy of Sciences of the Ukrainian Republic in 1961,and Academician of the Academy of Sciences of USSR in 1984. He was awarded the rank ofHonored Worker of Science and Engineering in 1961 and the title of Honored Professor by theSoros Foundation in 1994.

In the sixty years of his scientific activity, Mitropol’skii contributed to mathematical sciencewith fundamental results in the field of asymptotic methods of nonlinear analysis and promotedtheir applications to the investigation of nonlinear systems modeling real-world phenomena. Letus outline Mitropol’skii’s main scientific achievements.

A large series of Mitropol’skii’s papers (1948–64) contains further development of Krylov–Bogolyubov asymptotic methods. He comprehensively developed the algorithmic aspects of asymp-totic methods, suggested new schemes convenient for the practical construction of approximatesolutions (for systems with “small” and “large” parameters), and studied new physical phenomenatypical of nonlinear oscillation systems.

The papers published in 1949–50 deal with systematic and rigorous application of asymptoticmethods of nonlinear mechanics to the analysis of nonstationary processes in systems with dis-tributed parameters. In these papers, Mitropol’skii devised a general method for studying nonsta-tionary oscillations in systems with distributed parameters on the basis of the development andgeneralization of the one-frequency method on the one hand and the development of methods forsystems with slow parameters on the other hand.

A series of papers written by Mitropol’skii in 1950, 1955, and 1964 develops averaging methodsand their applications to the analysis of oscillation systems with slow parameters. A number ofresults were obtained by generalizing the averaging method to systems with deviating argument,which arise in the analysis of oscillations of mechanical, electromagnetic, and other nature (1966).

When considering solution sets admitted by complicated systems of nonlinear differential equa-tions, it is often important to single out a solution manifold (an integral manifold) whose dimensionis less than the order of the system and which has some specific properties. The solution of thisproblem involves proving the existence of an integral manifold of the system in question and an-alyzing the structure of this manifold and of some neighborhood of it. In this connection, specialattention is paid to constructive methods for approximating the vector function that specifies theintegral manifold and to the use of the approximate functions in qualitative analysis instead ofthe vector function defining the exact integral manifold. A rigorous theory of integral manifoldswas constructed for the first time by Bogolyubov (1945) for differential equations in the standardform

x = εX(t, x), where x and X are n-vectors and ε > 0 is a small parameter,

which arises in numerous problems of nonlinear mechanics.Mitropol’skii substantially developed the theory of integral manifolds (1958, 1969, 1973). In par-

ticular, he investigated integral manifolds of nonlinear differential equations with variable coeffi-cients, which permitted him to justify the one-frequency method for oscillation systems describedby nonlinear differential equations with slow parameters.

In the middle 1960s, Bogolyubov developed a new version of the method of successive changes ofvariables, which combines the method of accelerated convergence (typical for the Newton methodof tangents) and the method of integral manifolds. In the 1969 series of papers, Mitropol’skiisubstantially developed this method and applied it to the solution of a number of important prob-lems in nonlinear mechanics. For example, the method was used for the construction of a generalsolution of a system of nonlinear equations and the analysis of its behavior in a neighborhood ofsome quasiperiodic solution. Mitropol’skii also analyzed the possibility of reducing a nonlineardifferential system to a linear system with constant coefficients. The influence of random forces onnonlinear oscillation systems was analyzed in Mitropol’skii’s papers in 1980. He showed that theuse of asymptotic methods of nonlinear mechanics and the technique of Fokker–Plank–Kolmogorovequations has a great practical advantage over other methods, since it allows one to find thequadrature of the stationary distribution density of the amplitude and phase of random oscilla-tions. He also analyzed the possibility of using the averaging principle in stochastic differentialequations of the hyperbolic type (2003). He performed a large series of investigations (1988) forthe development of the group-theoretic approach in the averaging method. He proved necessaryand sufficient conditions for the decomposition of a higher-dimension system of ordinary differen-tial equations in subsystems of lower dimensions. These conditions can be constructively expressed

DIFFERENTIAL EQUATIONS Vol. 43 No. 1 2007

YURII ALEKSEEVICH MITROPOL’SKII 3

via coefficients of the system and can be reduced to the construction of Lie algebras (finite- orinfinite-dimensional). The possibility of expanding these algebras in a direct sum of ideals providesthe possibility of the decomposition. A series of Mitropol’skii’s papers deals with the investigationof the adiabatic invariance of nonlinear dynamical systems with a small parameter.

Mitropol’skii successfully combines his scientific and management activities. He pays muchattention to the education of young generation. His students include 100 Philosophy Doctors and25 Doctors of Sciences in physics and mathematics (in particular, 12 Philosophy Doctors fromVietnam, Uzbekistan, Georgia, Bulgaria, and Yugoslavia and 7 Doctors of Sciences from Vietnam,Uzbekistan, and Yugoslavia).

Mitropol’skii is a distinguished manager of science. Being Director of the Institute for Math-ematics, he contributed to opening new scientific departments, which stimulated research in thefield of algebra, theory of random processes, function theory, functional analysis, and mathematicalphysics. When Mitropol’skii was Director of the Institute for Mathematics for 30 years, about 500Philosophy Doctors and 80 Doctors of Sciences were trained there. His creative activity made theInstitute for Mathematics a leading center of mathematical research in Ukraine.

Mitropol’skii was Academician-Secretary of the Branch of Mathematics and Cybernetics in1963–83 and Academician-Secretary of the Branch of Mathematics and Member of the Presidiumof the Academy of Sciences of the Ukrainian Republic in 1983–93. Since 1992, he has been councillorat the Presidium of the National Academy of Sciences of Ukraine.

In 1965, Mitropol’skii won the Lenin Prize for achievements in the development of mathematicalscience and intensive pedagogical, scientific-organizational, and public activity. He was awardedthe State Prize of the Ukrainian Republic in 1980.

In 1986, he was awarded the title of Hero of Socialistic Labor and decorated with the Order ofLenin and the Gold Medal “Sickle and Hammer.” For the series of papers “Asymptotic Methodsof Nonlinear Mechanics,” Academy of Sciences of USSR awarded Mitropol’skii with the LyapunovGold Medal.

Mitropol’skii was awarded the Order of October Revolution (1971), the Order of the Red LaborBanner (1977), the Order of the Prince Yaroslav the Wise, rank V (1996), the Order of BogdanKhmelnitskii (2001), and the Order of the Prince Yaroslav the Wise, rank IV (2002).

His series of papers in nonlinear mechanics won the Krylov Prize (1969), the Lavrent’ev Prize(1985), and the Bogolyubov Prize (1993).

In 1981, the Cosmonautics Bureau of the USSR awarded Mitropol’skii the Medal of AcademicianYangel for permanent cooperation with Design Office “Yuzhnoe.”

Mitropol’skii also has authority in foreign countries. In 1971, he was elected Foreign Academicianof the Bologna Academy of Sciences, one of the oldest European Academies. He was awarded theSilver Medal “For Service in Science and Humanity” of the Czechoslovak Academy of Sciencesin 1977 and the Order “Friendship of Nations” of the Vietnam Socialistic Republic in 1984.

Until now Yurii Alekseevich Mitropol’skii is full of inexhaustible energy and continues to workwith enthusiasm on problems of nonlinear mechanics and theory of nonlinear differential equations.

We wish him good health and fruitful longevity.

I. V. Gaishun, N. A. Izobov, V. A. Il’in, V. S. Korolyuk,V. N. Koshlyakov, I. A. Lukovskii, V. M. Millionshchikov,

E. F. Mishchenko, S. I. Pokhozhaev, N. Kh. Rozov,A. M. Samoilenko, A. N. Sharkovskii, and A. B. Vasil’eva

LIST OF YU. A. MITROPOL’SKII’S MAIN PUBLICATIONS1

1987

265. Matematicheskie problemy nelineinoi mekhaniki (Mathematical Problems of Nonlinear Mechanics)(together with Samoilenko, A.M.), Kiev: Vishcha shkola.

266. On Periodic Solutions of Second-Order Wave Equations. III (together with Khoma, G.P.), Ukrain.Mat. Zh., vol. 39, no. 3, pp. 347–353.

1 The list of Mitropol’skii’s main publications prior to 1987 was published in Differ. Uravn., 1987, vol. 23, no. 1,pp. 3–9.



267. Mathematical Modelling of Dynamics of the Hydrogen Sulfide Zone of the Black Sea (together withBelyaev, V.I., Boguslavskii, S.G., and Berezovskii, A.A.), Vestn. Akad. Nauk USSR, no. 5, pp. 18–26.

268. Integriruemye dinamicheskie sistemy: spektral’nye i differentsial’no-geometricheskie aspekty(Integrable Dynamical Systems: Spectral and Differential-Geometric Aspects) (together with Bogo-lyubov, N.N. (jun.), Prikarpatskii, A.K., and Samoilenko, V.G.), Kiev: Naukova Dumka.

269. Integral Sets of a Class of Differential Equations with Sampled-Data Influence (together with Samoilen-ko, A.M. and Perestyuk, N.A.), Preprint Acad. Sci. USSR, Inst. Math., Kiev, no. 87.2.

270. Asymptotic Methods and Development of Nonlinear Mechanics, in: Mekhanika i nauchno-tekhnicheskiiprogress. T. 1. Obshchaya i prikladnaya mekhanika (Mechanics and Scientific and TechnologicalAdvance. Vol. 1. General and Applied Mechanics), Moscow: Nauka, pp. 72–87.

271. Asymptotic Solutions of a Multidimensional Nonlinear Wave Equation (together with M. V. Shul’ga),Dokl. Akad. Nauk , vol. 295, no. 1, pp. 30–33.

272. Stefan Problems with a Limit Stationary State in Special Electrometallurgy, Cold Cautery, and Physicsof Sea (together with Berezovskii, A.A.), Mat. Fiz. Nelin. Mekh., no. 7(41), pp. 50–60.

1988

273. Asymptotic Solutions of a Multidimensional Nonlinear Wave Equation (together with Shul’ga, M.V.),Soviet Math. Dokl., vol. 36, no. 1, pp. 23–26.

274. On Periodic Solutions of Second-Order Wave Equations. IV (together with Khoma, G.P.), Ukrain.Mat. Zh., vol. 40, no. 6, pp. 757–763.

275. Asymptotic Decomposition of Completely Integrable Pfaff Systems with a Small Parameter (togetherwith Lopatin, A.K.), Ukrain. Mat. Zh., vol. 40, no. 3, pp. 349–356.

276. Teoretiko-gruppovoi podkhod v asimptoticheskikh metodakh nelineinoi mekhaniki (Group-Theoretic Ap-proach in Asymptotic Methods of Nonlinear Mechanics) (together with Lopatin, A.K.), Kiev: NaukovaDumka.

277. Algebraic Scheme of Discrete Approximations of Linear and Nonlinear Dynamical Systems of Mathe-matical Physics (together with Prikarpatskii, A.K. and Samoilenko, V.G.), Ukrain. Mat. Zh., vol. 40,no. 4, pp. 453–459.

278. Influence of Random Forces on Hyroscopic Systems (together with Nasyrov, F.U.), Ukrain. Mat. Zh.,vol. 40, no. 5, pp. 592–599.

279. Dynamical Systems and Related Differential-Geometric Structures (together with Samoilenko, V.G.and Fil’, B.N.), Preprint Acad. Sci. USSR, Inst. Math., Kiev, no. 87.65.

280. On the Use of the Averaging Method in the Investigation of Hyperbolic Sampled-Data Systems(together with Rogovchenko, S.P.), Preprint Acad. Sci. USSR, Inst. Math., Kiev, no. 88.33.

281. Mathematical Investigation of Modern Problems of Power Industry (together with Berezovskii, A.A.and Plotnitskii, T.A.), in Matematicheskie problemy energetiki: Sb. nauchn. tr. (MathematicalProblems of Power Industry. Collection of Scientific Works), Kiev: Naukova Dumka, pp. 4–28.

282. On Some Results and Topical Problems of Theory of Periodic Motions of Nonlinear Mechanics (Review)(together with Martynyuk, A.A.), Prikl. Mekh., vol. 24, no. 3, pp. 3–14.

283. Asymptotic Decomposition of Completely Integrable Pfaff Systems with a Small Parameter (togetherwith Lopatin, A.K.), Ukrain. Mat. Zh., vol. 40, no. 3, pp. 349–356.

284. The Influence of Random Forces on Hyroscopic Systems (together with Nasyrov, F.U.), Ukrain. Mat.Zh., vol. 40, no. 5, pp. 592–599.

285. Algebraic Scheme of Discrete Approximations of Linear and Nonlinear Dynamical Systems of Mathe-matical Physics (together with Prikarpatskii, A.K. and Samoilenko, V.G.), Ukrain. Mat. Zh., vol. 40,pp. 453–459.



1989

286. The Influence of External Periodic Forces on a Harmonic Oscillator with a Sampled-Data Influence(together with Elgondyev, K.K.), Preprint Acad. Sci. USSR. Inst. Math., Kiev, no. 89.52.

287. Stefan Problem in Metallurgy, Cryosurgery, and Physics of Sea (together with Berezovskii, A.A.),Preprint Acad. Sci. USSR. Inst. Math., Kiev, no. 89.11.

288. Some Problems of Invariant Manifolds and Alternating Lyapunov Functions (together with Grod, I.N.),Preprint Acad. Sci. USSR. Inst. Math., Kiev, no. 89.8.

289. On the Effectiveness of the Use of Asymptotic Methods for Quasiwave Equations of Hyperbolic Type(together with Khoma, G.P.), Preprint Acad. Sci. USSR. Inst. Math., Kiev, no. 89.15.

290. On the Behavior of Solutions of Nonlinear Systems of Finite-Difference Equations in a Neighborhoodof an Invariant Toroidal Manifold (together with Martynyuk, D.I. and Danilov, V.Ya.), Ukrain. Mat.Zh., vol. 41, no. 1, pp. 56–63.

291. Bogolyubov’s Investigations in the Field of Mathematics and Theoretical Physics (together with Vladi-mirov, V.S., Parasyuk, O.S., and Petrina, D.Ya.), Ukrain. Mat. Zh., vol. 41, no. 9, pp. 1156–1164.

1990

292. Krylov–Bogolyubov Ideas in Differential Equations and Mathematical Physics, Their Development:A Report on the First Session of the Kiev Mathematical Society, June 6, 1989, Ukrain. Mat. Zh.,vol. 42, no. 3, pp. 291–302.

293. Issledovanie dikhotomii lineinykh sistem differentsial’nykh uravnenii c pomoshch’yu funktsii Lyapunova(The Investigation of the Dichotomy of Linear Systems of Differential Equations with the Use ofLyapunov Functions) (together with Samoilenko, A.M. and Kulik, V.L.), Kiev: Naukova Dumka.

294. A Remark on Adiabatic Invariant, Mat. Fiz. Nelin. Mekh., issue 14(48), pp. 1–30.

295. Adiabatic Invariant for a Double Pendulum with Slowly Changing Lengths, Mat. Fiz. Nelin. Mekh.,issue 14(48), pp. 30–39.

296. On a Two-Point Problem for Systems of Hyperbolic Equations (together with Urmancheva, L.B.),Ukrain. Mat. Zh., vol. 42, no. 12, pp. 1657–1663.

1991

297. Asimptoticheskie metody issledovaniya kvazivolnovykh uravnenii giperbolicheskogo tipa (AsymptoticMethods for Quasiwave Equations of Hyperbolic Type) (together with Khoma, G.P. andGromyak, M.I.), Kiev: Naukova Dumka.

298. On the Solvability of Boundary Value Problems of Electromagnetic Elasticity with Memory (togetherwith Kurbanov, I.), Dokl. Akad. Nauk SSSR, vol. 317, no. 1, pp. 35–39.

299. Oscillations in First-Order Delay Systems (together with Nguen Dong An’ and Nguen Tien Khii),Ukrain. Mat. Zh., vol. 43, no. 9, pp. 1193–1201.

300. On a Class of Nonlinear Oscillation Systems Admitting Exact Solutions of the Fokker–Plank–Kolmo-gorov Equations (together with Nguen Tien Khii), Ukrain. Mat. Zh., vol. 43, no. 10, pp. 1383–1388.

301. Approximate Symmetry of a Nonlinear Heat Equation (together with Shul’ga, M.V.), Ukrain. Mat.Zh., vol. 43, no. 6, pp. 833–837.

302. Symplectic Analysis of Dynamical Systems with a Small Parameter. New Criterion for the Stabiliza-tion of Homoclinic Separatrices (together with Antonishin, I.O., Prikarpatskii, A.K., and Samoilen-ko, V.G.), Preprint Inst. Math. Acad. Scie. Ukraine, Kiev, no. 91.53.

303. Aspects of Gradient–Holonomic Algorithm in Integrability Theory of Nonlinear Dynamical Systemsand Problems of Computer Algebra (together with Prikarpatskii, A.K., and Fil’, B.M.), Ukrain. Mat.Zh., vol. 43, no. 1, pp. 78–91.



1992

304. Metod usredneniya v issledovaniyakh rezonansnykh sistem (Averaging Method in Investigation of Res-onance Systems) (together with Grebenikov, E.A.), Moscow: Nauka.

305. Averaging of Sampled-Data Evolution Systems (together with Rogovchenko, Yu.V.), Ukrain. Mat.Zh., vol. 44, no. 1, pp. 76–83.

306. Nelineinye kolebaniya v kvazilineinykh dinamicheskikh sistemakh proizvol’nogo poryadka (NonlinearOscillations in Quasilinear Dynamical Systems of an Arbitrary Order) (together with Nguen Van Daoand Nguen Dong An), Kiev: Naukova Dumka.

307. Invariant Manifolds of Autonomous Differential Equations and Alternating Lyapunov Functions(together with Kulik, V.L.), Differ. Uravn., vol. 28, no. 3, pp. 398–405.

308. Symplectic Analysis of Dynamical Systems with a Small Parameter. New Stabilization Criterion forHomoclinic Separatrices (together with Antonishin, I.O., Prikarpatskii, A.K., and Samoilenko, V.G.),Ukrain. Mat. Zh., vol. 44, no. 1, pp. 46–66.

309. Problems with Free Boundaries for Nonlinear Evolution Equations in Problems of Metallurgy,Medicine, and Ecology (together with Berezovskii, A.A. and Plotnitskii, T.A.), Ukrain. Mat. Zh.,vol. 44, no. 1, pp. 67–76.

310. Adiabatic Invariants of Nonlinear Dynamical Systems (together with Antonishin, I.O. and Prikarpa-tskii, A.K.), Mat. Metody Fiz.-Mekh. Polya, no. 35, pp. 179–185.

1993

311. On the Boundedness of Motions of Nonlinear Weakly-Coupled Systems (together with Marty-nyuk, V.A.), Prikl. Mekh., vol. 29, no. 3, pp. 68–73.

312. On the Use of Asymptotic Methods in Substantially Nonlinear Stochastic Differential Equations(together with Kolomiets, V.G.), Mat. Fiz. Nelin. Mekh., vol. 18(52), pp. 52–54.

313. On Periodic Solutions of Second-Order Wave Equations (together with Khoma, G.P.), Ukrain. Mat.Zh., vol. 45, no. 8, pp. 1115–1121.

314. Investigation of the Classical Solvability of a Mixed Problem for a Second-Order Hyperbolic Equation(together with Khoma, L.G.), Ukrain. Mat. Zh., vol. 45, no. 9, pp. 1232–1238.

1994

315. Applied Asymptotic Methods in Nonlinear Oscillations (together with Nguen Van Dao), Hanoi.

316. Bogoliubov Averaging and Normalization Procedures in Nonlinear Mechanies. I (together with Lopa-tin, A.K.), Ukrain. Mat. Zh., vol. 46, no. 9, pp. 1171–1193.

317. Bogoliubov Averaging and Normalization Procedures in Nonlinear Mechanies. II (together with Lopa-tin, A.K.), Ukrain. Mat. Zh., vol. 46, no. 11, pp. 1509–1527.

318. Bogoliubov Averaging and Normalization Procedures in Nonlinear Mechanies. III (together withLopatin, A.K.), Ukrain. Mat. Zh., vol. 46, no. 12, pp. 1627–1641.

319. Free Boundary Problems for Nonlinear Evolution Equations in Metallurgy, Medicine and Ecology,Preprint Inst. Mat. Nats. Akad. Nauk Ukrain, Kiev, no. 94.20.

320. Asymptotic Methods in the Theory of Nonlinear Random Oscillations (together with Kolomiets, V.G.),Ukrain. Mat. Zh., vol. 46, no. 8, pp. 1011–1030.

321. Algebraic Structure of the Gradient-Holonomic Algorithm for Lax Integrable Nonlinear DynamicalSystems (together with Prykarpatsky, A.K., Samoilenko, V.Hr., Andrushkiw, R.I., and Prytula, M.M.),J. Math. Phys., vol. 35, no. 4, pp. 1763–1777.



1995

322. Nonlinear Mechanics, Groups and Symmetry (together with Lopatin, A.K.), Kluwer Academic Pub-lishers.

323. On the Approximate Solution of the Fokker–Plank–Kolmogorov Equation, Ukrain. Mat. Zh., vol. 47,no. 3, pp. 351–361.

324. On a Certain Nonlocal Problem for a Parabolic Equation (together with Shkhanukov, M.Kh. andBerezovskii, A.A.), Ukrain. Mat. Zh., vol. 47, no. 6, pp. 790–800.

325. Bogoliubov Averaging and Normalization Procedures in Nonlinear Mechanics. IV (together withLopatin, A.K.), Ukrain. Mat. Zh., vol. 47, no. 8, pp. 1044–1068.

326. On the Construction of an Asymptotic Solution of the Perturbed Klein–Gordon Equation, Ukrain.Mat. Zh., vol. 47, no. 9, pp. 1209–1216.

327. Periodic Solutions of Second-Order Quasilinear Hyperbolic Equations (together with Khoma, G.P.),Ukrain Mat. Zh., vol. 47, no. 10, pp. 1370–1375.

328. Nelineinaya mekhanika. Asimptoticheskie metody (Nonlinear Mechanics. Asymptotic Methods), Kiev:Inst. Math.

1996

329. Some Problems in the Development of Nonlinear Mechanics Theory and Applications, Facta Univ.Ser. Mech., vol. 5, pp. 539–560.

330. Space-Time Localization in Problems with Assembled Boundary for a Nonlinear Second-Order Equa-tion (together with Berezovskii, A.A. and Shkhanukov, M.Kh.), Ukrain. Mat. Zh., vol. 48, no. 2,pp. 202–211.

331. On Application of Asymptotic Methods of Nonlinear Mechanics for Solving Some Problems of Oscilla-tion Theory, Published by the University of Nis, Serbia, Yugoslavia Facta Universitatic, vol. 2, no. 6,pp. 1–9.

1997

332. Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type (together with Khoma,G. and Gromyak, M.), Kluwer Academic Publishers.

333. Problems with Arbitrary Boundaries and Nonlocal Problems for Nonlinear Parabolic Equations(together with Berezovskii, A.A.), Ukrain. Mat. Zh., vol. 49, no. 1, pp. 84–97.

334. Nonlinear Nonlocal Problems for a Parabolic Equation in a Two-Dimensional Domain (together withBerezovskii, A.A. and Shkhanukov–Lavshiev, M.Kh.), Ukrain. Mat. Zh., vol. 49, no. 2, pp. 244–254.

335. Periodic Problem for an Inhomogeneous Equation of String Oscillations (together with Khoma, G.P.and Tsinaik, P.V.), Ukrain. Mat. Zh., vol. 49, no. 4, pp. 558–565.

336. Nelineinaya mekhanika. Odnochastotnye kolebaniya (Nonlinear Mechanics. Single-Frequency Oscilla-tions), Kiev.

337. Applied Asymptotic Methods in Nonlinear Oscillations , (together with Nguyen Van Dao), KluwerAcademic Publishers, vol. 55.

338. Role of a Small Parameter and Perturbation Theory in Problems of Celestial Mechanics, Proceedingsof the Sixth National Congress on Mechanics. Hanoi, 3–5 December 1997 , Hanoi, pp. 141–150.

339. Asymptotic Decomposition Method as Development of Bogoliubov Averaging Method, NonlinearAnal., vol. 30, no. 8, pp. 5203–5210.

340. Nonlinear Mechanics. Symmetry Groups (together with Lopatin, A.K.), Netherlands: Kluwer.



1998

341. On the Construction of an Asymptotic Solution of the Perturbed Bretherton Equation, Ukrain Mat.Zh., vol. 50, no. 1, pp. 58–71.

342. A Remark on Asymptotic Approximations to Slow Wave Processes in Nonlinear Dispersive Media(together with Limarchenko, O.S.), Ukrain. Mat. Zh., vol. 50, no. 3, pp. 357–372.

343. On the Stabilization of Ateb Functions for Asymptotic Solutions of the Nonlinear Klein–GordonEquation (together with Sokol, B.I.), Ukrain. Mat. Zh., vol. 50, no. 5, pp. 665–671.

344. Solvability Conditions for Quasilinear Periodic Boundary Value Problems for a Second-Order Hyper-bolic Equation (together with Khoma, G.P. and Khoma, N.G.), Ukrain. Mat. Zh., vol. 50, no. 6,pp. 818–822.

345. Random Oscillations in the van-der-Pol System under the Influence of a Broadband Random Pro-cess (together with Nguen Dong An’ and Nguen Dyk T’in’), Ukrain. Mat. Zh., vol. 50, no. 11,pp. 1508–1512.

346. Asymptotic Methods for the Investigation of Some Nonlinear Equations Describing Wave Processes,Nonlinear Oscil., no. 1, pp. 20–29.

347. Nonlinear Mechanics (together with Samoilenko, A.M. and Lykova, O.B.), in Razvitie obshchei mekha-niki v Rossii i na Ukraine v 20-e gody XX veka (Development of General Mechanics in Russia andUkraine in 1920ies), Moscow; Kiev: Feniks, pp. 233–272.

348. Random Oscillations in the van-der-Pol System under the Influence of a Broadband Random Pro-cess (together with Nguen Dong An’ and Nguen Dyk T’in’), Ukrain. Mat. Zh., vol. 50, no. 11,pp. 1517–1521.

1999

349. Stabilization in Finite Time in Problems with Free Boundary for Some Classes of Second-Order Non-linear Equations (together with Berezovskii, A.A. and Shkhanukov–Lafishev, M.Kh.), Ukrain. Mat.Zh., vol. 51, no. 2, pp. 214–223.

350. Free Boundary Problems for Nonlinear Evolution Equations in Metallurgy, Medicine and Ecology(together with Berezovsky, A.A. and Berezovsky, S.A.), J. Math. Engng. Ind., vol. 7, no. 3,pp. 301–347.

351. Academician N. N. Bogolyubov. A Tribute in Honor of His 90th Birthday, Ukrain. Mat. Zh., vol. 51,no. 8, pp. 1012–1014.

352. Role Played by Nikolai Nikolaevich Bogolyubov in the Development of Theory of Nonlinear Oscilla-tions, Ukrain. Math. Zh., vol. 51, no. 8, pp. 1014–1036.

353. Vvedenie v rezonansnuyu analiticheskuyu dinamiku (Introduction to Resonance Analytic Dynamics),(together with Grebenikov, E.A. and Ryabov, Yu.A.), Moscow: Yanus-K.

2000

354. Basic Achievements of Academician N. N. Bogolyubov in the Field of Nonlinear Mechanics (KievPeriod of Bogolyubov’s Activity), Ukrain. Fiz. Zh., vol. 45, nos. 4–5, pp. 405–408.

355. On N. N. Bogolyubov’s Work in the Field of Nonlinear Mechanics, in Tr. Mat. in-ta im. V.A. Steklova:Problemy sovremennoi matematicheskoi fiziki (sb. statei) (Proceeding of the Steklov Mathemati-cal Institute: Problems of Modern Mathematical Physics. Collection of Papers), Moscow: Nauka,vol. 228, pp. 17–23.

356. Mathematical Modeling of Heat Transfer During Electron-Beam Autocrucible Melting by Means ofthe Steady-State Stefan Problem (together with Berezovsky, A.A. and Zhernovyl, Iu.V.), J. of Engin.Math., vol. 38, no. 2, pp. 173–190.

357. A Smooth Solution of the Dirichlet Problem for a Quasilinear Second-Order Hyperbolic Equation(together with Khoma, N.G. and Khoma, S.G.), Ukrain. Mat. Zh., vol. 52, no. 7, pp. 931–935.



358. N. N. Bogoloyubov’s Basic Achievements in the Field of Nonlinear Mechanics (Kiev Period of Bogo-lyubov’s Acitivity), Nonlinear Oscil., vol. 3, no. 2, pp. 148–153.

2001

359. Mathematical Modelling of Elastic Systems with a One-Sided External Influence (together with Li-marchenko, O.S., Matarazzo, G., and Toskano, L.), Problemy Upravlen. Inform., no. 5, pp. 48–70.

2003

360. Dichotomies and Stability in Nonautonomous Linear Systems (together with Samoilenko, A.M. andKulik, V.L.), London; New York: Taylor and Trancis.

361. Lectures on Asymptotic Methods of Nonlinear Dynamics (together with Nguyen Van Dao), Hanoi:Vietnam National University Publishing House.

362. On Asymptotic Solutions to Delay Differential Equation with Slowly Varying Coefficients (togetherwith Samoylenko, V.H. and Matarazzo, G.), Nonlinear Analysis , vol. 52, pp. 971–988.

363. On Averaging Principle in Stochastic Differential Equations of the Hyperbolic Type (together withKolomiets, V.G. and Kolomiets, O.V.), Ukrain. Mat. Zh., vol. 55, no. 5, pp. 711–715.

2004

364. Asymptotic Methods in Resonance Analytical Dynamics (together with Grebenikov, E.A. andRyabov, Y.A.), London.


yurii alekseevich mitropol’skii (a tribute in honor of his ninetieth birthday)

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