Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side

Abstract

We investigate the existence of mild solutions on a compact interval to some classes of semilinear neutral functional differential inclusions. We will rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler and on Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.