Research interests

  • impulsive systems
• retarded systems
• ordinary differential equations
• difference systems
• stability theory
 

Diplomas

1973: Honours Diploma in Mathematics at  Donetsk State University;
1980: Diploma of candidate of physical and mathematical sciences;
The theme of the candidate thesis is
"Some problems of the stability of dynamic systems".
1994: Diploma of doctor of physical and mathematical sciences. The theme of the candidate thesis is
"Methods of the study of the stability of nonautonomous systems".

Grants and awards

 

 

Career

Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine:
1974–76: Graduate student
1976: Engineer
1976–82:  Junior scientist
1982–95: Senior scientist
Since 1995:  Head scientist

 

Publications

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. Stability with respect to some of the variables under constantly acting perturbations. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1991, , no. 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. On the stability of invariant sets of a system of autonomous differential equations under continuous perturbations. (Russian) Ukraïn. Mat. Zh. 51 (1999), no. 9, 1287-1291; translation in Ukrainian Math. J. 51 (1999), no. 9, 1448-1453. (Co-author Konosevich, B. I.)
     
     
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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. The method of Lyapunov functions in problems of the stability of solutions of systems of differential equations with impulse action. (Russian) Mat. Sb. 194 (2003), no. 10, 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. On the stability of the zero solution of an almost periodic system of 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. On the stability of periodic systems with impulse action. (Russian) Mat. Zametki 76 (2004), no. 1, 44-51; translation in Math. Notes 76 (2004), no. 1-2, 41-47. (Co-author Gladilina, R. I.)
     
     
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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. On the asymptotic stability and instability of solutions of systems with impulse action. (Russian) Mat. Zametki 80 (2006), no. 4, 516-525; translation in Math. Notes 80 (2006), no. 3-4, 491-499. (Co-authors Ignatyev, O. A.; Soliman, A. A.)
     
     
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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. Asymptotic stability and instability with respect to part of the variable of solutions of systems with impulse action. (Russian) Sibirsk. Mat. Zh. 49 (2008), no. 1, 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. On the existence of a quadratic Lyapunov function for linear systems with impulse effect. (Russian), Ukraïn. Mat. Zh. 62 (2010), no. 11, 1451-1458.
     
     
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