On the Solution Set of Differential Inclusions with State Constraints

Abstract

In this paper we consider differential inclusions in R m with time varying state constraints, of the form: −x(t) eN (x(t)) K(t) + F(t,x(t)), x(0) ≡ x(0) Here N(x) denotes the normal cone to k(t)at x. We prove that the solution set of this inclusion is an Rδ-set in C(T,R m). For the special case when k(t)-K (independent of t), our result also characterizes the solution set of the projected differentional inclusion and also help us establish the existence of periodic trajectories