Abstract
In this paper we study different types of (generalized) solutions for semilinear evolution inclusions in general Banach spaces, called limit and weak solutions, which are extensions of the weak solutions studied by T. Donchev [Nonlinear Anal., 16 (1991), pp. 533--542] and the directional solutions studied by J. Tabor [Set-Valued Anal., 14 (2006), pp. 121--148]. Under appropriate assumptions, we show that the set of the limit solutions is compact $R_\delta$. When the right-hand side satisfies the one-sided Perron condition, a variant of the well-known lemma of Filippov--Plis, as well as a relaxation theorem, are proved.
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