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

Abstract

In this paper we prove the existence of solutions of the differential inclusions $$\left\{ \begin{gathered} \dot X(t) \in - A_t (X(t)) + F(t,X(t)),,0 \leqslant t \leqslant T_0 \hfill \\ X(0) = x_0 \hfill \\ \end{gathered} \right.$$ whereAt 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].