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

Amaria Arara, Mouffak Benchohra


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.

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