A property of the solution set of differential inclusions in banach spaces with a caratheodory orientor field

Abstract

We examine the solution set of differential inclusions in separable Banach spaces with a Caratheodory orientor field i.e. teF(t ,x) is measurable and xeF(t,x) is completely u.s.c. We show that the solution set is an Rδ set in C(T,X), extending this way earlier results by Lasry-Robert, Himmelberg-Van Vleck, De Blasi - Myjak and Papageorgiou