Journal of Convex Analysis 28 (2021), No. 4, 1137--1154
Copyright Heldermann Verlag 2021
Existence of Solutions Belonging to a Tube for Non-Convex Sweeping Processes
Wissam Latreche
Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri University, Constantine, Algeria
and: Laboratoire de Mathématique et Physique, Université de Perpignan, France
w.latreche@gmail.com
Oana Silvia Serea
Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, Bergen, Norway
and: Laboratoire de Mathématique et Physique, Université de Perpignan, France
oss@hvl.no
We establish existence results of solutions belonging to a tube for non-convex sweeping processes. Our approach mainly combines features belonging to the class of prox-regular sets, sweeping processes associated with this type of sets and fixed point theorems techniques.
Keywords: Differential inclusion, sweeping processes, solution tube, prox-regular sets, fixed point theorems.
MSC: 34A60, 47J20, 46N10.
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