Discussiones Mathematicae Differential Inclusions 15(2) (1995) 99-127

[BIBTex]

PERIODIC SOLUTIONS OF EVOLUTION PROBLEM ASSOCIATED WITH MOVING CONVEX SETS

Charles Castaing

Département de Mathématiques, Université Montpellier II,
Case 051, Place Eugéne Bataillon, 34095 Montpellier cedex 05, France

Manuel D.P. Monteiro Marques

Centro de Matemática e Aplicaçoes Fundamentais and
Faculdade de Ciencias da Universidade de Lisboa
Av. Prof. Gama Pinto, 2, P-1699 Lisboa Codex, Portugal

Abstract

This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form -Du∈NC(t)(u(t))+f(t, u(t)) where C is a T-periodic multifunction from [0, T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, NC(t)(u(t)) is the normal cone of C(t) at u(t), f:[0, T]×H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.

Keywords: evolution problem, periodic solution, sweeping process, perturbation, Lipschitzean, absolutely continuous, BV solution.

1991 Mathematics Subject Classification: 35K22, 34A60.

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