Nonconvex integro-differential sweeping processes involving maximal monotone operators

Abstract

This paper is devoted to the study of a perturbed differential inclusion governed by a nonconvex sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of an integral forcing term which the integrand depends on two time-variables and a maximal monotone operator. By using a semi-regularization method combined with a Gronwall-like inequality we prove solvability of the initial value problem.