On some boundary-value problems for functional-differential inclusions in Banach spaces

The general boundary-value problem for a semilinear functional-differential inclusion in a separable Banach space is considered. A many-valued integral operator whose fixed points are integral solutions to the problem is constructed. Conditions ensuring this many-valued operator to be condensing with respect to the vector measure of noncompactness are investigated. Application of topological degree theory allows one to establish some existence theorems for the boundary-value problem. The Cauchy problem and the periodic problem are considered as special cases.