A Controllability Problem for Causal Functional Inclusions with an Infinite Delay and Impulse Conditions

Abstract

In this paper we study the controllability problem in a Banach space for various classes of functional inclusions with causal operators with an infinite delay, and impulse effects. Basing on the topological degree theory for condensing multimaps, we prove a global theorem on the existence of trajectories for systems governed by functional inclusions. As an application, we obtain generalizations of existence theorems for the controllability problem for a semilinear first order functional differential inclusions of this type and a semilinear functional differential inclusions of a fractional order 0 < q < 1.