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 δ -set provided some appropriate conditions on the Banach space are imposed. Applications to the periodic problem for this type of inclusions are given.2010 Mathematics Subject Classification. 45D05, 45M15, 47H08, 47H10, 47H30.

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The paper is devoted to study the existence of periodic solutions for retarded differential inclusions. The nonsmooth guiding potential method is used and topological degree theory for multivalued maps is applied.The present paper concerns the existence of periodic solutions for differential inclusions with retarded arguments of the form (Q F ) .

The existence of solutions of some nonlocal initial value problems for differential inclusions is established. The guiding potential method is used and the topological degree theory for admissible multivalued vector fields is applied. Some conclusions concerning compactness of the solution set have been drawn.