Научные интересы

• прямой метод Ляпунова в теории устойчивости решений обыкновенных дифференциальных уравнений, функционально-дифференциальных уравнений с запаздыванием,  разностных уравнений и систем с импульсным воздействием
 

Дипломы

1973  – Диплом о высшем образовании по специальности  “математика”  Донецкого государственного университета
1980 – Диплом кандидата физико-математических наук по специальности 01.02.01 – теоретическая механика
Тема диссертации "Некоторые вопросы устойчивости динамических систем".
1994 – Диплом доктора физико-математических наук
Тема диссертации "Методы исследования устойчивости неавтономных систем".

Гранты и премии

 

 

Карьера

Институт прикладной математики и механики Национальной Академии наук Украины:
1974–76 гг. – аспирант
1976 г. – инженер
1976–82 гг. – младший научный сотрудник
1982–95 гг. – старший научный сотрудник
1995 г. – н / вр – ведущий научный сотрудник

Публикации

1. Investigations of the stability of axisymmetric top with liquid filling. (Russian) Prikl. Mekh. V.10. No. 8 (1974), 107-111. (Co-author Savchenko A.Ya.)
    
2. On the sufficient conditions of the stability of axisymmetric top with liquid filling. (Russian) Mekh. Tverd. Tela No. 9 (1977), 82-86.
    
3. Investigations of the stability domains of axisymmetric top with liquid filling. (Russian) Mekh. Tverd. Tela No. 9 (1977), 73-81. (Co-authors Margolis S.M.; Savchenko A.Ya.)
    
4. The effect of vanishing constantly acting perturbations on asymptotically stable motions. (Russian) Mekh. Tverd. Tela No. 11 (1979), 92-95.
    
5. On the question of the effect of constantly acting perturbations on nonasymptotically stable motions. (Russian) Theory of stability and its applications (Russian), pp. 31-38, 297, ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1979. (Co-author Savchenko, A. Ya. )
    
6. Stability in the critical case of q pairs of purely imaginary roots. (Russian) Mekh. Tverd. Tela No. 11 (1979), 95-98. (Co-authors Savchenko, A. Ya.; Svetlichnaja, N. V.)
    
7. Formal stability in a critical case of n pairs of purely imaginary roots. (Russian) Mekh. Tverd. Tela No. 12 (1980), 76-85.
    
8. On the question of stability in a singular case. (Russian) Mekh. Tverd. Tela No. 12 (1980), 72-76.
    
9. Continuous dependence of asymptotic stability on parameters in the critical case of n pairs of purely imaginary roots. (Russian) Mat. Fiz. No. 32 (1982), 8-9.
    
10. Stability in the critical case of a pair of purely imaginary roots for nonautonomous systems. (Russian) Mat. Fiz. No. 31 (1982), 27-32.
     
11. On stability of the equilibrium position of vibrational systems with variable coefficients. (Russian) J. Appl. Math. Mech. 46 (1982), no. 1, 167-168.
     
12. Some generalizations of the Barbashin-Krasovskiĭ theorems. (Russian) Mat. Fiz. No. 34 (1983), 19-22.
     
13. Investigation of the stability of steady motions of rigid bodies under the action of imbalances of a varying physical nature. (Russian) Stability of motion, 101-104, 252, ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1985. (Co-authors Bolgrabskaya, I. A.; Kononykhin, G. A.; Savchenko, A. Ya. )
     
14. Stability of uniform rotations of an absolutely rigid body with a fluid filling. (Russian) Mat. Fiz. Nelineĭn. Mekh. No. 5(39) (1986), 14-18. (Co-author Savchenko, A. Ya.)
     
15. On the asymptotic stability of a class of nonautonomous systems. (Russian) Differentsial’nye Uravneniya 23 (1987), no. 12, 2161-2163.
     
16. Investigation of the boundary of the domain of stability of the uniform rotations of a rigid body with a fluid filling. (Russian) Mekh. Tverd. Tela No. 19 (1987), 72-78. (Co-authors Ben’kovich, Yu. G.; Verbitskaya, N. V.)
     
17. Stability of motion with respect to some of the variables under constantly acting perturbations. (Russian) Mat. Fiz. Nelineĭn. Mekh. No. 10(44) (1988), 20-25.
     
18. Stability of almost periodic systems with respect to some of the variables. (Russian) Differentsial’nye Uravneniya 25 (1989), no. 8, 1446-1448.
     
19. Some problems in the stability of nonautonomous dynamical systems ``Naukova Dumka'', Kiev, 1989. 204 pp. ISBN: 5-12-000540-3. (Co-author Savchenko, A. Ya.)
     
20. Preservation of the property of uniform asymptotic stability with respect to some of the variables. (Russian) Prikl. Mat. Mekh. 53 (1989), no. 1, 167--171; translation in J. Appl. Math. Mech. 53 (1989), no. 1, 136-139
     
21. On the instability of the equilibrium position of a linear oscillator with variable parameters. (Russian) Prikl. Mat. Mekh. 55 (1991), no. 4, 701-703; translation in J. Appl. Math. Mech. 55 (1991), no. 4, 566-567.
     
     
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22. Устойчивость относительно части переменных при постоянно действующих возмущениях, Изв. вузов. Матем., 1991, № 2, 55–60; translation in Soviet Math. (Iz. VUZ) 35 (1991), no. 2, 63-69.
     
     
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23. Application of the direct Lyapunov method to the study of integral sets. (Russian) Ukraïn. Mat. Zh. 44 (1992), no. 10, 1342-1348; translation in Ukrainian Math. J. 44 (1992), no. 10, 1229-1235.
     
     
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24. On the existence of Lyapunov functions in problems of the stability of integral sets. (Russian) Ukraïn. Mat. Zh. 45 (1993), no. 7, 932-941; translation in Ukrainian Math. J. 45 (1993), no. 7, 1031-1041.
     
     
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25. Equi-asymptotic stability of integral sets. (Russian) Ukraïn. Mat. Zh. 47 (1995), no. 2, 180-185; translation in Ukrainian Math. J. 47 (1995), no. 2, 212-217.
     
26. On the asymptotic stability of integral sets. (Russian) Ukraïn. Mat. Zh. 48 (1996), no. 8, 1064-1073; translation in Ukrainian Math. J. 48 (1996), no. 8, 1202-1213.
     
27. On the Routh-Lyapunov-Salvadori stability criterion. (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1997, no. 10, 78-79. (Co-author Konosevich, B. I.)
     
28. Stability of a linear oscillator with variable parameters. Electron. J. Differential Equations 1997, No. 17, 6 pp. (electronic).
     
     
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29. On the stability of equilibrium for almost periodic systems. Nonlinear Anal. 29 (1997), no. 8, 957-962.
     
     
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30. Об устойчивости инвариантных множеств системы автономных дифференциальных уравнений при постоянно действующих возмущениях, Укр. мат. журн., 51 (1999), № 9, 1287-1291; translation in Ukrainian Math. J. 51 (1999), no. 9, 1448-1453. (Соавтор Б.И.Коносевич)
     
     
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31. On the asymptotic stability in functional-differential equations. Proc. Amer. Math. Soc. 127 (1999), no. 6, 1753-1760.
     
     
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32. Stability with respect to some of the variables in functional-differential systems with delay. (Russian) Mekh. Tverd. Tela No. 30 (2000), 158-165.
     
33. On the partial equiasymptotic stability in functional differential equations. J. Math. Anal. Appl. 268 (2002), no. 2, 615-628.
     
     
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34. Maximum and anti-maximum principles for the general operator of second order with variable coefficients. Appl. Math. Comput. 134 (2003), no. 1, 173-184. (Co-authors Barteneva, Irina V.; Cabada, Alberto)
     
35. On necessary and sufficient conditions for the asymptotic stability of impulsive systems. (Russian) Ukrain. Mat. Zh. 55 (2003), no. 8, 1035-1043; translation in Ukrainian Math. J. 55 (2003), no. 8, 1254-1264. (Co-author Gladilina, R. I.)
     
     
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36. On the stability of invariant sets of functional differential equations. Nonlinear Anal. 55 (2003), no. 6, 641-656. (Co-authors Bernfeld, Stephen R.; Corduneanu, Constantin)
     
     
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37. Метод функций Ляпунова в задачах устойчивости решений систем дифференциальных уравнений с импульсным воздействием, Матем. сб., 194:10 (2003), 117–132; translation in Sb. Math. 194 (2003), no. 9-10, 1543-1558.
     
     
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38. Asymptotic stability in functional differential equations with delay. Integral methods in science and engineering (Saint Etienne, 2002), 97-102, Birkhauser Boston, Boston, MA, 2004.
     
39. Stability of the zero solution of an almost periodic system of finite-difference equations. (Russian) Differ. Uravn. 40 (2004), no. 1, 98-103, 143; translation in Differ. Equ. 40 (2004), no. 1, 105-110.
     
     
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40. Об устойчивости периодических систем с импульсным воздействием, Матем. заметки, 76:1 (2004), 44–51; translation in Math. Notes 76 (2004), no. 1-2, 41-47. (Соавтор Р. И. Гладилина)
     
     
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41. Investigation of stability using Lyapunov functions with constant signs. (Russian) Ukr. Mat. Visn. 2 (2005), no. 1, 74-83, 147; translation in Ukr. Math. Bull. 2 (2005), no. 1, 77-86.
     
     
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42. Stability of invariant sets of functional differential equations with delay. Nonlinear Funct. Anal. Appl. 10 (2005), no. 1, 11-24. (Co-author Corduneanu, C.)
     
     
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43. Об асимптотической устойчивости и неустойчивости решений систем с импульсным воздействием”, Матем. заметки, 80:4 (2006), 516–525; translation in Math. Notes 80 (2006), no. 3-4, 491-499. (Соавторы: О. А. Игнатьев, А. А. Солиман)
     
     
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44. On the stability in periodic and almost periodic difference systems. J. Math. Anal. Appl. 313 (2006), no. 2, 678-688. (Co-author Ignatyev, O. A.)
     
     
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45. On the stability of discrete systems. Integral methods in science and engineering, 105-116, Birkhauser Boston, Boston, MA, 2006. (Co-author Ignatyev, O. A.)
     
46. On the preservation of the stability property of impulsive systems under perturbations. (Russian) Avtomat. i Telemekh. 2007, , no. 8, 78-85; translation in Autom. Remote Control 68 (2007), no. 8, 1364-1371. (Co-author Gladilina, R. I.)
     
     
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47. On the equiasymptotic stability of solutions of doubly periodic systems with impulse action. (Russian) Ukrain. Mat. Zh. 60 (2008), no. 10, 1317-1325; translation in Ukrainian Math. J. 60 (2008), no. 10, 1528-1539.
     
     
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48. On the stability of invariant sets of systems with impulse effect. Nonlinear Analysis. 69 (2008), no. 1, 53-72.
     
     
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49. Investigation of the asymptotic stability of solutions of systems with impulse effect. Int. J. Math. Game Theory Algebra 17 (2008), no. 3, 141-164. (Co-author Ignatyev, O. A.)
     
50. Об асимптотической устойчивости и неустойчивости относительно части переменных решений систем с импульсным воздействием, Сиб. матем. журн., 49:1 (2008), 125–133; translation in Sib. Math. J. 49 (2008), no. 1, 102-108.
     
     
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51. Lyapunov's second method in problems of the stability of solutions of systems with impulse effect. Proceedings in Applied Mathematics and Mechanics. – 2008, p. 2030031-2030032.
     
     
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52. Stability of solutions of systems with impulse effect. Progress in nonlinear analysis research, 363-389, Nova Sci. Publ., New York, 2009. (Co-author Ignatyev, O. A.)
     
     
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53. Necessary and sufficient stability conditions for invariant sets of nonlinear impulsive systems, Int. Appl. Mech., vol. 44, no. 2, 2008, 228-237. (Co-author Gladilina, R. I.)
     
     
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54. Comments on “On stability of switched homogeneous nonlinear systems” by Lijun Zhang, Sheng Liu, and Hai Lan [J. Math. Anal. Appl. 334 (1) (2007) 414–430], J. Math. Anal. Appl. 373 , 2011, 343–344.
     
     
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55. Quadratic forms as Lyapunov functions in the study of stability of solutions to difference equations, Electron. J. Differential Equations, vol. 2011 (2011), no. 19, 1–21.
     
     
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56. О существовании функции Ляпунова в виде квадратичной формы для линейных систем дифференциальных уравнений с импульсным воздействием, Укр. мат. журн., 2010, т. 62, № 11, 1451-1458.
     
     
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