Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 99-109

Integral manifolds of impulsive differential equations

D. D. Bainov,1 S. I. Kostadinov,1 N. Van Minh,2 N. Hong Thai,2 and P. P. Zabreiko2

1Department of Mathematics, Plovdiv University, Bulgaria
2Department of Mathematics, Byelorussian University, Minsk, Russia

Received 1 February 1991; Revised 1 March 1991

Copyright © 1992 D. D. Bainov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper is concerned with the existence of integral manifolds of impulsive differential equations as t+. Under the assumption of exponential trichotomy on the linear part of the right-hand side of the equation, it is proved that if the nonlinear perturbation is small enough, then there exist integral manifolds as t+ for the perturbed equations.