Non-instantaneous Impulsive Semilinear Differential Inclusions

Abstract

we are concerned by finding the conditions that ensure the existence of mild solution for non-instantaneous impulsive semilinear differential inclusions, where the linear part is the infinitesimal generator of a C0-semigroup in infinite dimensional Banach space . We do not assume that this C0-semigroup is compact, instead we assume that the nonlinear part is a multivalued function satisfies a condition expressed in a measure of compactness. We will consider the case when the values of the multiv