PORTUGALIAE MATHEMATICA Vol. 54, No. 4, pp. 485507 (1997) 

Topological Properties of Solution Sets for Sweeping Processes with DelayCharles Castaing and Manuel D.P. Monteiro MarquesDépartement de Mathématiques, Université Montpellier II,case 051, Place Eugène Bataillon, F34095 Montpellier cedex 05  FRANCE C.M.A.F. and Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex  PORTUGAL Abstract: Let $r>0$ be a finite delay and ${\cal C}_0={\cal C}([r,0],H)$ the Banach space of continuous vectorvalued functions defined on $[r,0]$ taking values in a real separable Hilbert space $H$. This paper is concerned with topological properties of solution sets for the functional differential inclusion of sweeping process type: $$ {du\over dt} \in N_{K(t)}(u(t))+F(t,u_t), $$ where $K$ is a $\gamma$Lipschitzean multifunction from $[0,T]$ to the set of nonempty compact convex subsets of $H\!$, $N_{K(t)}(u(t))$ is the normal cone to $K(t)$ at $u(t)$ and $F:[0,T]\times{\cal C}_0\rightarrow H$ is an upper semicontinuous convex weakly compact valued multifunction. As an application, we obtain periodic solutions to such functional differential inclusions, when $K$ is $T$periodic, i.e. when $K(0)=K(T)$ with $T\geq r$. Keywords: Functional differential inclusion; normal cone; Lipschitzean mapping; sweeping process; perturbation; delay. Classification (MSC2000): 35K22, 34A60 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1997 Sociedade Portuguesa de Matemática
