Georgian Mathematical Journal 13 (2006), No. 2, 239--249
Copyright Heldermann Verlag 2006
Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
Messaoud Bounkhel
Dept. of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
bounkhel@ksu.edu.sa
[Abstract-pdf]
We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturbation and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of the form $\dot u(t)\in C(u(t))$, $\ddot u(t)\in -N^P(C(u(t))$; $\dot u(t))+F(t,\dot u_t)$ when $C$ is a nonconvex bounded Lipschitz set-valued mapping and $F$ is a set-valued mapping with convex compact values taking their values in finite dimensional spaces.
Keywords: Uniformly prox-regular set, nonconvex sweeping processes, delay, differential inclusions.
MSC: 49J52, 46N10, 58C20
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