Existence Results of Nonconvex Differential Inclusions

Messaoud Bounkhel

Abstract: This paper is devoted to the study of nonconvex differential inclusions by using some concepts of regularity in nonsmooth analysis. In section 2, we prove that the nonconvex sweeping process introduced by J.J. Moreau in 1970's has the same set of solutions of a differential inclusion with convex compact values. Using this result, we deduce, in section 3, some existence results in the finite dimensional setting of the nonconvex sweeping process. In section 4, we introduce a new concept of uniform regularity over sets for functions to prove the existence of viable solutions for another type of nonconvex differential inclusions.

Keywords: sweeping process; directional regularity; Fréchet normal regularity.

Classification (MSC2000): 34A60, 34G25, 49J52, 49J53.

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