Impulsive semilinear differential inclusions: Topological structure of the solution set and solutions on non-compact domains Original Research Article

This paper deals with an impulsive Cauchy problem governed by the semilinear evolution differential inclusion x′(t)∈A(t)x(t)+F(t,x(t))x′(t)∈A(t)x(t)+F(t,x(t)), where {A(t)}t∈[0,b]{A(t)}t∈[0,b] is a family of linear operators (not necessarily bounded) in a Banach space EE generating an evolution operator and FF is a Carathéodory type multifunction. First a theorem on the compactness of the set of all mild solutions for the problem is given. Then this result is applied to obtain the existence of mild solutions for the impulsive Cauchy problem defined on non-compact domains.