Relaxation Results for Nonlinear Evolution Inclusions with One-sided Perron Right-hand Side

In a Banach space X, we study the evolution inclusion of the form x ^′(t)∈A x(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-Pli? lemma is also proved.