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. tεF(t ,x) is measurable and xεF(t,x) is completely u.s.c. We show that the solution set is an R_δ set in C(T,X), extending this way earlier results by Lasry-Robert, Himmelberg-Van Vleck, De Blasi - Myjak and Papageorgiou

Keywords:

• Banach space
• orienter fields
• differential inclusions

AMS(MOS)::

• 34G05