Samoilenko Anatoly Mykhailovych

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Total publications: 58
Scientific articles: 42

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Abstract pages:7177
Full texts:2370
Doctor of physico-mathematical sciences (1968)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 2.01.1938
Keywords: theory of perturbations of invariant manifolds; multifrequency oscillations; Green function for the problem of invariant torus; linear extensions of dynamical systems on a torus; asymptotic methods of nonlinear mechanics; averaging methods; methods of accelerated convergence; impulsive systems; boundary-value problems.


The scientific interests cover problems related to the investigation of the behavior of integral curves on invariant toroidal and compact manifolds and in their neighborhoods, the development of the theory of perturbations of toroidal manifolds, the development of asymptotic methods and creation of new methods for investigations in nonlinear mechanics. The notion of the Green function of the problem on the invariant torus of a linear extension of a dynamical system on a torus was introduced. Fundamental results were obtained in the theory of impulsive differential systems. For the investigation of periodic problems for systems of ordinary differential equations, the "numerical-analytic method" was proposed, which was further generalized to a broad class of boundary-value problems.


Graduated from the Department of Mechanics and Mathematics at the Shevchenko Kiev State University in 1960. Defended the Candidate-Degree Thesis in 1963 and Doctoral-Degree Thesis in 1967. Worked as a senior scientific researcher at the Institute of Mathematics in 1965–1974. A professor since 1974. The head of the Chair of Differential Equations at the Shevchenko Kiev State University in 1974–1987. The Director of the Institute of Mathematics of the Ukrainian National Academy of Sciences since 1988. Elected to become a Corresponding Member of the Ukrainian National Academy of Sciences in 1978 and Full Academician in 1995. I am the author of more than 400 scientific works, among which there are 16 monographs and 10 textbooks. I give lectures at the Shevchenko Kiev State University and National Technical University "KPI."

Decorated with an order of Friendship of Peoples (1984) and a diploma of the Presidium of the Supreme Soviet of the Ukraine (1987). Awarded the State Prize of the Ukraine in the field of Science and Engineering (1985 and 1996), the N. Krylov Prize (1981) and N. Bogolyubov Prize (1998) of the Ukrainian National Academy of Sciences. Awarded the title of "Soros Professor" in 1996 and the title of "Honored Personality of Science and Technology of Ukraine" in 1998.

Main publications:
  • Ronto M., Samoilenko A. M. Numerical-Analytic Methods in the Theory of Boundary-Value Problems. Singapore: World Scientific Publishing Co., 2000. x+455 pp.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. O. D. Artemovych, A. Ballester-Bolinches, M. R. Dixon, F. de Giovanni, R. I. Grigorchuk, V. V. Kirichenko, L. A. Kurdachenko, V. S. Monakhov, J. Otal, M. O. Perestyuk, A. P. Petravchuk, M. V. Pratsiovytyi, A. M. Samoilenko, A. N. Skiba, I. Ya. Subbotin, E. I. Zelmanov, A. V. Zhuchok, Yu. V. Zhuchok, “Nicolai N. Semko (dedicated to 60-th Birthday)”, Algebra Discrete Math., 24:1 (2017),  C–F  mathnet
2. A. M. Samoilenko, A. N. Stanzhytskyi, “On the averaging of differential equations on an infinite interval”, Differ. Uravn., 42:4 (2006),  476–482  mathnet  mathscinet; Differ. Equ., 42:4 (2006), 505–511
3. A. M. Samoilenko, A. N. Stanzhytskyi, “The Reduction Principle in Stability Theory of Invariant Sets of Itô Stochastic Systems”, Differ. Uravn., 38:5 (2002),  631–636  mathnet  mathscinet; Differ. Equ., 38:5 (2002), 663–668
4. A. A. Abramenko, V. I. Lahno, A. M. Samoilenko, “Group Classification of Nonlinear Evolutionary Equations: II. Invariance Under Solvable Groups of Local Transformations”, Differ. Uravn., 38:4 (2002),  482–489  mathnet  mathscinet; Differ. Equ., 38:4 (2002), 502–509
5. V. I. Lahno, A. M. Samoilenko, “Group Classification of Nonlinear Evolution Equations: I. Invariance Under Semisimple Local Transformation Groups”, Differ. Uravn., 38:3 (2002),  365–372  mathnet  mathscinet; Differ. Equ., 38:3 (2002), 384–391
6. A. M. Samoilenko, A. A. Boichuk, L. I. Karandzhulov, “Fredholm Boundary Value Problems with a Singular Perturbation”, Differ. Uravn., 37:9 (2001),  1186–1193  mathnet  mathscinet; Differ. Equ., 37:9 (2001), 1243–1251
7. A. M. Samoilenko, A. A. Burilko, I. N. Grod, “Moduli of continuity of the derivatives of invariant tori for linear extensions of dynamical systems”, Differ. Uravn., 36:1 (2000),  103–113  mathnet  mathscinet; Differ. Equ., 36:1 (2000), 120–131
8. A. M. Samoilenko, Yu. V. Teplinskii, “Limit theorems in the theory of periodic solutions of linear and quasilinear systems of difference equations”, Differ. Uravn., 35:9 (1999),  1262–1270  mathnet  mathscinet; Differ. Equ., 35:9 (1999), 1277–1285
9. Ya. I. Bigun, A. M. Samoilenko, “Justification of the averaging principle for multifrequency systems of differential equations with delay”, Differ. Uravn., 35:1 (1999),  8–14  mathnet  mathscinet; Differ. Equ., 35:1 (1999), 6–13
10. A. M. Samoilenko, A. N. Stanzhytskyi, “On invariant sets of differential equations with small random perturbations”, Differ. Uravn., 34:1 (1998),  54–58  mathnet  mathscinet; Differ. Equ., 34:1 (1998), 54–58
11. A. M. Samoilenko, V. L. Kulik, “On the properties of matritsants that affect the regularity of linear extensions of dynamical systems on a torus”, Differ. Uravn., 33:5 (1997),  684–688  mathnet  mathscinet; Differ. Equ., 33:5 (1997), 687–691
12. A. M. Samoilenko, V. L. Kulik, “On the regularity of differential equations that are linearized with respect to some of the variables”, Differ. Uravn., 31:5 (1995),  773–777  mathnet  mathscinet; Differ. Equ., 31:5 (1995), 715–718
13. A. A. Boichuk, V. F. Zhuravlyov, A. M. Samoilenko, “Linear Noetherian boundary value problems for impulse differential systems with delay”, Differ. Uravn., 30:10 (1994),  1677–1682  mathnet  mathscinet; Differ. Equ., 30:10 (1994), 1546–1551
14. A. M. Samoilenko, Yu. V. Teplinskii, “On the smoothness of an invariant torus of a countable linear extension of a dynamical system on an $m$-dimensional torus”, Differ. Uravn., 30:5 (1994),  781–790  mathnet  mathscinet; Differ. Equ., 30:5 (1994), 717–725
15. A. M. Samoilenko, Yu. V. Teplinskii, “The truncation method in the construction of invariant tori of countable systems of differential equations”, Differ. Uravn., 30:2 (1994),  204–212  mathnet  mathscinet; Differ. Equ., 30:2 (1994), 184–192
16. A. M. Samoilenko, “N. N. Bogolyubov and non-linear mechanics”, Uspekhi Mat. Nauk, 49:5(299) (1994),  103–146  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:5 (1994), 109–154  isi
17. A. M. Samoilenko, S. I. Trofimchuk, “Almost periodic impulse systems”, Differ. Uravn., 29:5 (1993),  799–808  mathnet  mathscinet; Differ. Equ., 29:5 (1993), 684–691
18. A. A. Boichuk, N. A. Perestyuk, A. M. Samoilenko, “Periodic solutions of impulse differential systems in critical cases”, Differ. Uravn., 27:9 (1991),  1516–1521  mathnet  mathscinet  zmath; Differ. Equ., 27:9 (1991), 1070–1073
19. A. M. Samoilenko, V. L. Kulik, “Systems of linear differential equations that are regular on the whole axis”, Differ. Uravn., 26:8 (1990),  1338–1343  mathnet  mathscinet; Differ. Equ., 26:8 (1990), 979–984
20. A. M. Samoilenko, R. I. Petrishin, “On integral manifolds of multifrequency oscillatory systems”, Izv. Akad. Nauk SSSR Ser. Mat., 54:2 (1990),  378–395  mathnet  mathscinet  zmath; Math. USSR-Izv., 36:2 (1991), 391–409
21. A. M. Samoilenko, R. I. Petrishin, “The averaging method in some boundary value problems”, Differ. Uravn., 25:6 (1989),  956–964  mathnet  mathscinet; Differ. Equ., 25:6 (1989), 688–695
22. A. M. Samoilenko, “On the question of the justification of the averaging method for multifrequency oscillating systems”, Differ. Uravn., 23:2 (1987),  267–278  mathnet  mathscinet
23. A. M. Samoilenko, Yu. V. Teplinskii, “Invariant tori of differential systems with impulses in spaces of bounded numerical sequences”, Differ. Uravn., 21:8 (1985),  1353–1361  mathnet  mathscinet
24. Yu. A. Mitropol'skii, A. M. Samoilenko, V. L. Kulik, “Application of quadratic forms to the study of systems of linear differential equations”, Differ. Uravn., 21:5 (1985),  776–788  mathnet  mathscinet
25. A. M. Samoilenko, Yu. V. Teplinskii, N. S. Tsyganovsky, “Behavior of solutions of a quasilinear system of differential equations with impulses in the neighborhood of an invariant torus”, Differ. Uravn., 18:5 (1982),  833–839  mathnet  mathscinet
26. A. M. Samoilenko, N. A. Perestyuk, “On the stability of solutions of systems with impulse action”, Differ. Uravn., 17:11 (1981),  1995–2001  mathnet  mathscinet
27. A. M. Samoilenko, “Necessary conditions for the existence of invariant tori of linear extensions of dynamical systems on a torus”, Differ. Uravn., 16:8 (1980),  1427–1437  mathnet  mathscinet  zmath
28. A. M. Samoilenko, O. D. Nurzhanov, “The Bubnov–Galerkin method for construction of periodic solutions of a Volterra type integro-differential equation”, Differ. Uravn., 15:8 (1979),  1503–1517  mathnet  mathscinet
29. A. M. Samoilenko, V. L. Kulik, “Exponential dichotomy of an invariant torus of dynamical systems”, Differ. Uravn., 15:8 (1979),  1434–1443  mathnet  mathscinet  zmath
30. A. M. Samoilenko, N. A. Perestyuk, “Periodic solutions of weakly nonlinear systems with impulse action”, Differ. Uravn., 14:6 (1978),  1034–1045  mathnet  mathscinet  zmath
31. A. M. Samoilenko, N. A. Perestyuk, “Stability of the solutions of differential equations with impulsive action”, Differ. Uravn., 13:11 (1977),  1981–1992  mathnet  mathscinet  zmath
32. A. M. Samoilenko, I. V. Polesya, “The existence of separatrix surfaces for systems in standard form”, Differ. Uravn., 11:10 (1975),  1827–1831  mathnet  mathscinet  zmath
33. A. M. Samoilenko, I. V. Polesya, “Occurrence of invariant sets in the neighborhood of the equilibrium position”, Differ. Uravn., 11:8 (1975),  1409–1415  mathnet  mathscinet  zmath
34. A. M. Samoilenko, “The exponential stability of an invariant torus of a dynamical system”, Differ. Uravn., 11:5 (1975),  820–834  mathnet  mathscinet  zmath
35. A. M. Samoilenko, N. A. Perestyuk, “N. N. Bogoljubov's second theorem for systems of differential equations with impulse action”, Differ. Uravn., 10:11 (1974),  2001–2009  mathnet  mathscinet  zmath
36. A. M. Samoilenko, D. I. Martynyuk, N. A. Perestyuk, “Existence of invariant tori for systems of difference equations”, Differ. Uravn., 9:10 (1973),  1904–1910  mathnet  mathscinet  zmath
37. A. M. Samoilenko, “On the reduction to canonical form of a dynamical system in the neighborhood of a smooth invariant torus”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972),  209–233  mathnet  mathscinet  zmath; Math. USSR-Izv., 6:1 (1972), 211–234
38. A. M. Samoilenko, “Preservation of an invariant torus under perturbation”, Izv. Akad. Nauk SSSR Ser. Mat., 34:6 (1970),  1219–1240  mathnet  mathscinet  zmath; Math. USSR-Izv., 4:6 (1970), 1225–1249
39. A. M. Samoilenko, “The equivalence of a smooth function to a Taylor polynomial in the neighborhood of a finite-type critical point”, Funktsional. Anal. i Prilozhen., 2:4 (1968),  63–69  mathnet  mathscinet  zmath; Funct. Anal. Appl., 2:4 (1968), 318–323
40. A. M. Samoilenko, “Periodic solutions of second-order nonlinear equations”, Differ. Uravn., 3:11 (1967),  1903–1912  mathnet  mathscinet  zmath
41. A. D. Myshkis, A. M. Samoilenko, “Systems with shocks at prescribed instants of time”, Mat. Sb. (N.S.), 74(116):2 (1967),  202–208  mathnet  mathscinet; Math. USSR-Sb., 3:2 (1967), 187–193
42. A. M. Samoilenko, “Reducibility of a system of ordinary differential equations in a neighborhood of a smooth toroidal manifold”, Izv. Akad. Nauk SSSR Ser. Mat., 30:5 (1966),  1047–1072  mathnet  mathscinet  zmath

43. Yu. A. Drozd, V. V. Kirichenko, L. A. Kurdachenko, F. M. Lyman, M. O. Perestyuk, A. P. Petravchuk, A. M. Samoilenko, M. M. Semko, L. A. Shemetkov, I. Ya. Subbotin, V. I. Sushchansky, V. V. Sharko, “To the 100$^{th}$ anniversary of the birth of Sergei Nikolaevich Chernikov”, Algebra Discrete Math., 13:2 (2012),  C–F  mathnet
44. Yu. A. Drozd, V. V. Kirichenko, L. A. Kurdachenko, F. M. Lyman, M. O. Perestyuk, A. M. Samoilenko, M. M. Semko, I. Ya. Subbotin, V. I. Sushchansky, V. V. Sharko, “To the memory of D. I. Zaitsev”, Algebra Discrete Math., 13:1 (2012),  C–D  mathnet  mathscinet
45. Yu. M. Berezanskii, V. E. Zakharov, V. P. Kotlyarov, K. V. Maslov, S. P. Novikov, L. A. Pastur, F. S. Rofe-Beketov, A. M. Samoilenko, E. Ya. Khruslov, “Vladimir Aleksandrovich Marchenko (on his 90th birthday)”, Uspekhi Mat. Nauk, 67:5(407) (2012),  186–191  mathnet  mathscinet  elib; Russian Math. Surveys, 67:5 (2012), 967–972  isi
46. D. V. Anosov, V. S. Afraimovich, L. A. Bunimovich, S. V. Gonchenko, V. Z. Grines, Yu. S. Ilyashenko, A. B. Katok, S. A. Kashchenko, V. V. Kozlov, L. M. Lerman, A. D. Morozov, A. I. Neishtadt, Ya. B. Pesin, A. M. Samoilenko, Ya. G. Sinai, D. V. Treschev, D. V. Turaev, A. N. Sharkovskii, A. L. Shil'nikov, “Leonid Pavlovich Shil'nikov (obituary)”, Uspekhi Mat. Nauk, 67:3(405) (2012),  175–178  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 67:3 (2012), 573–577  isi
47. A. V. Arutyunov, Yu. N. Bibikov, F. P. Vasil'ev, I. V. Gaishun, S. V. Emel'yanov, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, S. A. Mazanik, E. K. Makarov, A. A. Martynyuk, E. F. Mishchenko, E. I. Moiseev, Yu. S. Osipov, V. A. Pliss, N. Kh. Rozov, V. A. Sadovnichy, A. M. Samoilenko, T. K. Shemjakina, “Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)”, Differ. Uravn., 46:1 (2010),  3–8  mathnet  mathscinet  zmath; Differ. Equ., 46:1 (2010), 1–7
48. A. Ballester-Bolinches, R. I. Grigorchuk, M. R. Dixon, Yu. A. Drozd, V. V. Kirichenko, J. Otal, M. A. Perestyuk, A. P. Petravchuk, N. V. Polyakov, A. M. Samoilenko, N. N. Semko, V. V. Sharko, L. A. Shemetkov, A. N. Skiba, I. Ya. Subbotin, V. I. Sushchansky, E. I. Zel'manov, “Leonid A. Kurdachenko: to the 60th birthday”, Algebra Discrete Math., 2009, 4,  E–H  mathnet
49. Yu. M. Berezanskii, V. P. Kotlyarov, V. A. Marchenko, K. V. Maslov, S. P. Novikov, F. S. Rofe-Beketov, A. M. Samoilenko, Ya. G. Sinai, E. Ya. Khruslov, M. V. Shcherbina, “Leonid Andreevich Pastur (to his 70th brithday)”, Uspekhi Mat. Nauk, 63:1(379) (2008),  190–191  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:1 (2008), 197–199  isi
50. V. I. Andriychuk, V. A. Artamonov, V. M. Babych, O. O. Bezushchak, V. M. Bondarenko, M. A. Dokuchaev, Yu. A. Drozd, V. M. Futornyi, M. F. Gorodniy, R. I. Grigorchuk, N. M. Gubareni, P. M. Gudivok, A. I. Kashu, M. Komarnytskyi, L. A. Kurdachenko, F. M. Lyman, V. V. Lyubashenko, V. S. Mazorchuk, V. V. Nekrashevych, B. V. Novikov, A. S. Oliynyk, A. Yu. Ol'shanskii, S. A. Ovsienko, M. O. Perestyuk, A. P. Petravchuk, V. M. Petrychkovych, A. M. Samoilenko, M. M. Semko, V. V. Sergeichuk, V. V. Sharko, L. A. Shemetkov, I. P. Shestakov, V. I. Sushchansky, P. D. Varbanets, E. I. Zel'manov, V. N. Zhuravlyov, “Vladimir Kirichenko (on his 65th birthday)”, Algebra Discrete Math., 2007, 4,  E–H  mathnet
51. A. V. Arutyunov, S. V. Emel'yanov, N. A. Izobov, V. A. Il'in, S. K. Korovin, V. I. Korzyuk, A. M. Samoilenko, V. T. Borukhov, O. I. Kostyukova, T. K. Shemjakina, N. J. Yurchuk, “Ivan Vasil'evich Gaishun (A tribute in honor of his sixtieth birthday)”, Differ. Uravn., 42:10 (2006),  1299–1306  mathnet  mathscinet; Differ. Equ., 42:10 (2006), 1365–1373
52. V. N. Abrashin, I. V. Gaishun, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, A. A. Martynyuk, V. M. Millionshchikov, Yu. A. Mitropol'skii, V. A. Pliss, N. Kh. Rozov, A. A. Samarskii, A. M. Samoilenko, T. K. Shemjakina, “Nikolai Alekseevich Izobov”, Differ. Uravn., 36:1 (2000),  3–11  mathnet  mathscinet; Differ. Equ., 36:1 (2000), 1–11
53. Yu. A. Mitropol'skii, S. M. Nikol'skii, A. M. Samoilenko, S. A. Telyakovskii, “Nikolai Pavlovich Korneichuk (on his 80th birthday)”, Uspekhi Mat. Nauk, 55:6(336) (2000),  183–184  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:6 (2000), 1205–1207  isi
54. D. V. Anosov, V. S. Vladimirov, I. V. Gaishun, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, V. A. Kondratiev, L. D. Kudryavtsev, Yu. A. Mitropol'skii, E. F. Mishchenko, O. A. Oleinik, V. A. Pliss, M. I. Rakhimberdiev, N. Kh. Rozov, A. M. Samoilenko, A. F. Filippov, T. K. Shemjakina, “Vladimir Mikhaǐlovich Millionshchikov (on the occasion of his sixtieth birthday)”, Differ. Uravn., 35:10 (1999),  1299–1312  mathnet  mathscinet; Differ. Equ., 35:10 (1999), 1311–1327
55. N. A. Izobov, V. A. Il'in, N. N. Krasovskii, V. M. Matrosov, A. A. Samarskii, A. M. Samoilenko, “Ivan Vasil'evich Gaǐshun (on the occasion of his fiftieth birthday)”, Differ. Uravn., 33:6 (1997),  723–729  mathnet  mathscinet; Differ. Equ., 33:6 (1997), 723–732
56. V. A. Il'in, N. A. Izobov, A. A. Martynyuk, A. M. Samoilenko, “Yuriǐ Alekseevich Mitropol'skiǐ (on the occasion of his eightieth birthday)”, Differ. Uravn., 33:1 (1997),  3–5  mathnet  mathscinet; Differ. Equ., 33:1 (1997), 1–3
57. V. S. Vladimirov, E. F. Mishchenko, O. A. Oleinik, Yu. S. Osipov, A. M. Samoilenko, K. V. Frolov, “Yurii Alekseevich Mitropol'skii (on his 80th birthday)”, Uspekhi Mat. Nauk, 52:1(313) (1997),  237–239  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:1 (1997), 233–236  isi
58. N. N. Bogolyubov, E. F. Mishchenko, A. M. Samoilenko, “Yurii Alekseevich Mitropol'skii (on his seventieth birthday)”, Uspekhi Mat. Nauk, 42:4(256) (1987),  193–195  mathnet  mathscinet; Russian Math. Surveys, 42:4 (1987), 155–159  isi
59. N. N. Bogolyubov, V. S. Korolyuk, A. M. Samoilenko, “Yurii Alekseevich Mitropol'skii (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 32:1(193) (1977),  217–228  mathnet  mathscinet  zmath; Russian Math. Surveys, 32:1 (1977), 157–170

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