Abstract
In a Banach space X, we study the evolution inclusion of the form x′(t)∈Ax(t)+F(t,x(t)), where A is an m-dissipative operator and F is an almost lower semicontinuous multifunction with nonempty closed values. If F is one-sided Perron with sublinear growth, then, we establish the relation between the solutions of the considered differential inclusion and the solutions of the relaxed one, i.e., \(x^{\prime} (t)\in Ax (t)+\overline{co}F (t,x (t) )\). A variant of the well known Filippov-Pliś lemma is also proved.
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