Abstract:In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x'(t)\in -A x(t)+f(t,x(t))$, $x(0)=x_0$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.
Keywords: $m$-accretive operators, measures of noncompactness, differential inclusions, semigroups of contractions
AMS Subject Classification: 58D25, 47H20, 47H09