Periodic Mild Solutions of Infinite Delay not Instantaneous Impulsive Evolution Inclusions

Abstract

This paper deals with the existence of periodic mild solutions for a class of functional evolution inclusions. We use a multivalued fixed point theorem in Banach spaces combined with the technique of measure of noncompactness. We show that the Poincare operator is a condensing operator with respect to Kuratowski’s measure of noncompactness in a determined phase space, and then derive periodic solutions from bounded solutions by using Sadovskii’s fixed point theorem.