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) εN (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 R_δ-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

Keywords:

• Differential inclusion
• normal cone. R_δset

AMS(MOS):

• 34A34
• 34A60