Lower semi-continuous nonconvex perturbation of m-accrative differential inclusions in Banach spaces

In this paper we prove the existence of solutions of the differential inclusions $$left{ begin{gathered} dot X(t) in - A_t (X(t)) + F(t,X(t)),,0 leqslant t leqslant T_0 hfill X(0) = x_0 hfill end{gathered} right.$$ whereA _t is a multivaluedm-accretive operator on a Banach spaceE andF is a measurable multifunction defined on the set (G = overline {{ (t,x):A_t (x) ne 0/} } ) , lower semicontinuous inx and its values are not necessarily convex inE. This result generalizes some results in [1] and [9].