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Volume 6,     Number 2,     Summer 1998

 

ON THE TRANSLATION MULTIOPERATOR
ALONG THE SOLUTIONS OF SEMILINEAR
DIFFERENTIAL INCLUSIONS IN BANACH SPACES
MICHAIL KAMENSKI. VALERI OBUKHOVSKI AND PIETRO ZECCA

Abstract. 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.

 

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