Electron. J. Diff. Equ., Vol. 2012 (2012), No. 168, pp. 1-6.

Existence of solutions for convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces

Messaoud Bounkhel

We show the existence of at least one Lipschitz solution for extensions of convex sweeping processes in reflexive smooth Banach spaces. Our resultis proved under a weaker assumption on the moving set than those in [3], and using a different discretization.

Submitted February 14, 2012. Published October 4, 2012.
Math Subject Classifications: 34A60, 49J53.
Key Words: Uniformly smooth and uniformly convex Banach spaces; state dependent sweeping process; generalized projection; duality mapping

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Messaoud Bounkhel
King Saud University, Department of Mathematics
P.O. Box 2455, Riyadh 11451, Riyadh, Saudi-Arabia
email: bounkhel@ksu.edu.sa, bounkhel_messaoud@yahoo.fr

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