Lipschitz multivalued perturbations of integro-differential prox-regular sweeping processes

TL;DR

This paper establishes an existence theorem for Lipschitz multivalued perturbations of integro-differential sweeping processes involving prox-regular sets in Hilbert spaces, with applications to various scientific and engineering problems.

Contribution

It introduces a general existence theorem for solutions to perturbed integro-differential sweeping processes with nonconvex multivalued Lipschitz perturbations.

Findings

Existence of solutions under Lipschitz multivalued perturbations.

Applicability to complementarity problems and electrical circuits.

Extension to nonconvex set-valued perturbations.

Abstract

Integro-differential sweeping processes with prox-regular sets in Hilbert spaces have been the subject of various recent studies. Diverse applications of such differential inclusions to complementarity problems, electrical circuits, frictionless contact, can be found in the literature. Here we provide a general theorem of existence of solution for such processes perturbed by a Lipschitz multimapping with nonconvex values.