Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 2, Pages 179-190

A class of singularly perturbed evolution systems

N. U. Ahmed

University of Ottawa, Department of Mathematics and Department of Electrical Engineering, 161 Louis Pasteur, Ontario, Ottawa KIN 6N5, Canada

Received 1 November 1993; Revised 1 May 1994

Copyright © 1994 N. U. Ahmed. 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.


In this paper we study a class of evolution equations where the semigroup generators are singularly perturbed by a nonnegative real valued function of time. Sufficient conditions for existence of evolution operators and their compactness are given including continuous dependence on the perturbation. Further, for a coupled system of singularly perturbed semilinear systems in two Banach spaces, existence of periodic solutions and their stability are studied.