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Keywords:
$m$-accretive operators; measures of noncompactness; differential inclusions; semigroups of contractions
$m$-accretive operators; measures of noncompactness; differential inclusions; semigroups of contractions
Summary:
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.
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