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Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 137-146
http://dx.doi.org/10.1155/S1048953391000102

Existence of periodic solutions of impulsive differential systems

1Department of Mathematics, University of Alberta, Alberta, Edmonton T6G 2G1, Canada
2Department of Applied Mathematics, University of Waterloo, Ontario, Waterloo N2L 3G1, Canada

Received 1 October 1990; Revised 1 January 1991

Copyright © 1991 Hindawi Publishing Corporation. 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.

Abstract

In this paper, the existence of periodic solutions of impulsive differential systems is considered. Since the solutions of such a system are peicewise continuous, it is necessary to introduce piecewise continuous Lyapunov functions. By means of such functions, together with the comparison principle, some sufficient conditions for the existence of periodic solutions of impulsive differential systems are established.