Existence results for the Darboux problem for hyperbolic differential inclusions in Banach spaces

Анотація

In this paper we investigate the existence of solutions to the Darboux problem for a third order hyperbolic differential and functional differential inclusion with nonconvex-valued right-hand side. We shall rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler and on Schaefer’s fixed point theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with non-empty closed and decomposable values.