Structure of the solution set to Volterra integral inclusions and applications

Abstract

The topological and geometric structure of the solution set to Volterra integral inclusions in Banach spaces is investigated. It is shown that the set of solutions in the sense of Aumann integral is nonempty compact acyclic in the space of continuous functions or is even an $R_{\delta }$-set provided some appropriate conditions on the Banach space are imposed. Applications to the periodic problem for this type of inclusions are given.