Journal of Applied Mathematics and Stochastic Analysis 
Volume 7 (1994), Issue 2, Pages 179-190
doi:10.1155/S1048953394000183

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

Abstract

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.