Impulsive Evolution Inclusions

Abstract

In this chapter, the existence of mild solutions for impulsive differential inclusions in a reflexive Banach space is obtained. Weakly compact valued nonlinear terms are considered, combined with strongly continuous evolution operators generated by the linear part. A continuation principle or a fixed point theorem are used, according to the various regularity and growth conditions assumed. Secondly, a topological structure of the set of solutions to impulsive functional differential inclusions on the half-line is investigated. It is shown that the solution set is nonempty, compact and, moreover, an \(R_\delta \) -set. It is proved on compact intervals and then, using the inverse limit method , obtained on the half-line.