On the solution sets of differential inclusions and the periodic problem in Banach spaces

Abstract In this paper, the topological structure of the solution set of a constrained semilinear differential inclusion in a Banach space E is studied. It is shown that the set of all mild solutions, with values in a closed and, in general, thin subset D ⊂ E , is an R δ -set provided natural boundary conditions and appropriate geometrical assumptions on D (which hold, e.g. when D is convex) are satisfied. Applications to the periodic problem and to the existence of equilibria are given.

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