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Journal of Convex Analysis 27 (2020), No. 3, 833--844
Copyright Heldermann Verlag 2020

Existence of Solutions for Sweeping Processes with Local Conditions

Ba Khiet Le
Institute of Engineering Sciences, University of O'Higgins, Rancagua, Chile

Sweeping processes, introduced by J. J. Moreau, have been studied significantly in recent years due to their interesting applications in practice. However, most of the researches use the global Hausdorff distance to describe the movement of the moving set, which is probably not satisfied for unbounded cases. In this paper, we study the existence of solutions for sweeping processes by using only local excess condition. The result obtained can be applied to analyze a class of time-varying evolution variational inequalities.

Keywords: Existence of solutions, sweeping processes, local excess condition, time-varying evolution variational inequalities.

MSC: 47H05, 46N10, 47H04.

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