General Existence Results for Second Order Nonconvex Sweeping Process with Unbounded Perturbations

Messaoud Bounkhel

Abstract: This paper is devoted to study the existence of solutions for general second order sweeping processes with perturbations of the form $\dot x(t)\in K(x(t))$, $\ddot x(t)\in-N(K(x(t));\dot x(t))+F(t,x(t),\dot x(t))+G(t,x(t),\dot x(t))$, where $K$ is a nonconvex set-valued mapping with compact values, $F$ is an unbounded scalarly upper semicontinuous convex set-valued mapping, and $G$ is an unbounded continuous non convex set-valued mapping taking their values in separable Hilbert spaces.

Keywords: uniformly prox-regular set; normal cone; subdifferential; second order nonconvex sweeping processes.

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

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