Existence of solutions on compact and non-compact intervals for impulsive semilinear differential inclusions with delay

In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilinear differential inclusion. The family of linear operators that gives the linear part of the differential inclusion is supposed to generate an evolution operator and the nonlinear part is an upper Carathéodory type multifunction. We first provide the existence of mild solutions on a compact interval and the compactness of the solution set. Then we apply this result to obtain the existence of mild solutions for the impulsive Cauchy problem on non-compact intervals.