Controllability for a Class of Degenerate Functional Differential Inclusions in a Banach Space

Abstract

We study the controllability problem for a system governed by a degenerate semilinear functional differential inclusion in a Banach space with infinite delay. Notice that we are not assuming that the generalized semigroup generated by the linear part of inclusion is compact. Instead we suppose that the multivalued nonlinearity satisfies the regularity condition expressed in terms of the Hausdorff measure of noncompactness. It allows to obtain the general controllability principle in the terms of the topological degree theory for condensing multivalued operators. Two realizations of this principle are considered.

Controllability Results for Impulsive Neutral Evolution Differential Systems

“…On the other hand, the concept of controllability is of great importance in mathematical control theory. Controllability for differential systems in Banach spaces under the assumption of compactness and noncompactness of the operator semigroups has been studied by many authors [1,6,7,9,10,13,18,20,21,23,24,27] by using various fixed point theorems. In particular, by using Monch fixed point theorem, Guo et al [10] established the sufficient conditions for the controllability of the following class of impulsive evolution inclusions with nonlocal conditions:…”