Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 99-109
Integral manifolds of impulsive differential equations
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 . 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 for the perturbed equations.