Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions.

In this paper we prove the existence of a mild solution for a semi- linear evolution dierential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator gen- erated by the family operators. Also, we prove that the set of mild solutions is compact.

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