Alexander Rezounenko

List of principal publications (last updated Jan 27, 2012)

2. I.D. Chueshov, A.V. Rezounenko, Global attractors for a class of retarded quasilinear partial differential equations// Matematicheskaya fizika, analiz, geometriya. -1995. N.1 (3). -P.363-383.

3. A.V. Rezunenko, A quasistatic variant of a problem on delayed oscillations// Dopov. Nats. Acad. Nauk Ukraine -1997. no. 3, 41-45. (Title of the journal in English - "Reports of the National Academy of Sciences of Ukraine").

4. A.V. Rezounenko, On singular limit dynamics for a class of retarded nonlinear partial differential equations// Matematicheskaya fizika, analiz, geometriya. -1997. N.4 (1/2). -P.193-211.

5. L. Boutet de Monvel, I.D. Chueshov and A.V. Rezounenko, Long-timebe haviour of strong solutions for a class of retarded nonlinear P.D.E.s// Communications in Partial Differential Equations. -1997. -N.22(9,10). -P.1453-1474.

6. L. Boutet de Monvel, I.D. Chueshov and A.V. Rezounenko, Inertial manifolds for retarded semilinear parabolic equations // Nonlinear Analysis: Theory, Methods and Applications. -1998. N.34. -P.907-925.

7. A.V. Rezounenko, Inertial Manifolds with Delay for Retarded Semilinear Parabolic Equations // Discrete and Continuous Dynamical Systems. -2000.- Vol. 6, N. 4. P.829-840.

8. G.M. Sklyar, A.V. Rezounenko, Stability of a strongly stabilizing control for systems with a skew-adjoint operator in Hilbert space // Journal of Mathematical Analysis and Applications.- 2001. -Vol. 254, N. 1. -P.1-11.

9. A.V. Rezounenko, On boundary value problem for a class of retarded nonlinear partial differential equations // Journal of Mathematical Analysis and Applications.- 2001. -Vol. 254, N. 2. -P.515-523.

10. G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls // C.R. Acad. Sci. Paris, Ser.I   -2001. Vol. 333. P.807-812.

11. A.V. Rezounenko, A sufficient condition for the existence of approximate inertial manifolds containing the global attractor // C.R. Acad. Sci. Paris, Ser.I .   -2002. Vol. 334, issue 11, P.1015-1020. ( This journal has new title Comptes Rendus Mathematique, but to cite an article use "C.R. Acad. Sci. Paris, Ser.I  " as before).

12. A.V. Rezounenko, Steady approximate inertial manifolds of exponential order for semilinear parabolic equations // Differential and Integral Equations.   -2002. Vol. 15. No. 11. P.1345-1356.

13. A.V. Rezounenko, Inertial manifolds for retarded second order in time evolution equations // Nonlinear Analysis: Theory, Methods and Applications.   -2002. Vol. 51, Issue 6, P. 1045-1054.

14. R. Rabah, G.M. Sklyar, A.V. Rezounenko, Generalized Riesz basis property in the analysis of neutral type systems // C.R. Acad. Sci. Paris, Ser.I .   -2003. Vol. 337. Issue 1, -P. 19-24 .

15. A.V. Rezounenko, Approximate inertial manifolds for retarded semilinear parabolic equations // Journal of Mathematical Analysis and Applications. -2003. Vol. 282, Issue 2, -P. 614-628.

16. G.M. Sklyar, A.V. Rezounenko, Strong asymptotic stability and constructing of stabilizing controls // Matematicheskaya fizika, analiz, geometriya. -2003. Vol.10, No. 4. -P.569-582.

17. R. Rabah, G.M. Sklyar, A.V. Rezounenko, On strong stability and stabilizability of linear systems of neutral type // in "Advances in time-delay systems", Ser. Lecture Notes in Computational Science and Engineering (LNCSE). Springer.-2004. Vol.38. -P.257-268.

18. A.V. Rezounenko, Investigations of retarded PDEs of second order in time using the method of Inertial manifolds with delay // Annales de l'Institut Fourier. -2004. Vol. 54. Issue 5, P.1547-1564.

19. R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space // Journal of Differential Equations. -2005. Vol. 214, Issue 2 , P. 391-428.

20. A.V. Rezounenko, J. Wu, A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors // Journal of Computational and Applied Mathematics. -2006. Vol. 190, Issues 1-2, (1 June 2006), P.99-113.

21. A.V. Rezounenko, Partial differential equations with discrete and distributed state-dependent delays // Journal of Mathematical Analysis and Applications. -2007. Vol. 326, Issue 2, (15 February 2007), P.1031-1045.

22. R. Rabah, G.M. Sklyar, A.V. Rezounenko, On strong regular stabilizability for linear neutral type systems // Journal of Differential Equations. - 2008. Vol. 245, Issue 3, (1 August 2008), P. 569-593. (Preprint RI2006-5, IRCCyN/EMN, Nantes, France, June 2006, 29 p.)

23. A.V. Rezounenko, Stability of positive solutions of local partial differential equations with a nonlinear integral delay term // Electronic Journal of Qualitative Theory of Differential Equations. Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 17. (2008), P. 1-7.

24. A.V. Rezounenko, On a class of P.D.E.s with nonlinear distributed in space and time state-dependent delay terms // Mathematical Methods in the Applied Sciences. - 2008. Vol. 31, Issue 13 (10 September 2008), P.1569-1585. (Published Online : Jan 21, 2008 ). [ Zbl 1148.35095 ].

25. A.V. Rezounenko, Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions // Nonlinear Analysis: Theory, Methods and Applications. - 2009. Volume 70, Issue 11 (1 June 2009), P.3978-3986. [ Zbl 1163.35494 ].

26. A.V. Rezounenko, Non-linear partial differential equations with discrete state-dependent delays in a metric space // Nonlinear Analysis: Theory, Methods and Applications. - 2010. Volume 73, Number 6 (15 September 2010) P.1707-1714. [ Zbl 1194.35488 ].

27. A.V. Rezounenko, Non-local PDEs with a state-dependent delay term presented by Stieltjes integral // C. R. Acad. Sci. Paris, Ser. I (Comptes Rendus Mathematique). -2011. Volume 349, Issues 3-4 (February 2011), P. 179-183. ( http://dx.doi.org/10.1016/j.crma.2011.01.012 ); [ Zbl 1213.35236 ].

28. A.V. Rezounenko, A condition on delay for differential equations with discrete state-dependent delay // Journal of Mathematical Analysis and Applications. - 2012. Volume 385, Issue 1 (1 January 2012) P. 506-516 (doi: 10.1016/j.jmaa.2011.06.070, available online 1 July 2011). [ Zbl 1242.34136 ].     File: pdf.

       Lecture Notes

29. A.V. Rezounenko, A short introduction to the theory of ordinary delay differential equations. Lecture Notes. Kharkov University Press. Kharkov. 2004. 41 p. (in Russian)

30. A.V. Rezounenko, Elementary properties of differential equations with a state-dependent delay. Lecture Notes. Kharkov University Press. Kharkov. 2010. 44 p. (in Russian)

       Book chapter(s)

31. R. Rabah, G.M. Sklyar, A.V. Rezounenko, On Pole Assignment and Stabilizability of Neutral Type Systems, in "Topics in Time Delay Systems", Lecture Notes in Control and Information Sciences, Volume 388/2009, Springer Berlin / Heidelberg ( ISSN 0170-8643, DOI 10.1007/978-3-642-02897-7 ), Pages 85-93.

Mathematics

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