On the translation multioperator along the solutions of semilinear differential inclusions in Banach spaces.

We give sufficient conditions under which the translation operator along the mild solutions of a semilinear differential inclusion in a Banach space is condensing with respect to the Hausdorff measure of noncompactness. It makes it possible to apply the topological degree theory for condensing multimaps to the existence of periodic solutions. We prove also F.E. Browder's type periodic existence theorem under some additional assumptions which guarantee that a mild solution is a Caratheodory one.