A Cauchy Type Problem for Causal Functional Inclusions in Banach Spaces

Abstract

In this paper, we study a Cauchy type problem in Banach spaces for various classes of functional inclusions with causal multioperators. Based 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 a Cauchy type problem for semilinear second order differential inclusions of this type and semilinear differential inclusions of the fractional order 1<q<2.