Delay Differential Inclusions with Constraints

Abstract

Abstract. In this paper we examine functional differential inclusions with memory and state constraints. For the case of time-independent state constraints, we show that the solution set is R¿ under Carathéodory conditions on the orientor field. For the case of time-dependent state constraints we prove two existence theorems. For this second case, the question of whether the solution set is R¿ remains open.

Semistability of Nonlinear Systems Having a Connected Set of Equilibria and Time-Delays

“…Note that (6) represents a set-valued differential equation called differential inclusion in the literature [30], [31]. In fact, (6) is a delay differential inclusion [32].…”

Periodic solutions of differential inclusions with retards

“…It should be noted that the existence of periodic solutions for functional differential inclusions satisfying Nagumo type tangential condition has been established by Haddad-Lasry [14] (autonomous case) and Hu-Papageorgiou [15] (nonautonomous case).…”

“…The acyclicity of S F is an important property since it allows us to use the topological degree theory for the Poincaré operator P F . The structure of the solution set for retarded and functional differential inclusions was investigated by Lasry-Robert [18], [19], Haddad [13], Haddad-Lasry [14] and recently Hu-Papageorgiou [15].…”