NONSTANDARD IMPULSIVE EVOLUTION EQUATIONS IN BANACH SPACES

Abstract

In this paper we consider a class of nonstandard linear impulsive evolution equations driven by vector measures. The principal operator (not necessarily bounded) is assumed to be the in¯nitesimal generator of the so called m-times integrated semigroup or more generally m-times integrated solution family. This includes the classical C0 semigroups and goes beyond covering a very large class of systems. We prove the existence and regularity properties of solutions for these systems. The paper is concluded with a brief discussion on some open problems.