Generalized Solutions of Semilinear Evolution Inclusions
研究了一般Banach空间中半线性发展包含的极限解和弱解，证明了极限解集是紧Rδ集，并在单侧Perron条件下证明了Filippov-Plis引理的变体及松弛定理。
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.