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An Existence Result for Discontinuous Second-Order Nonconvex State-Dependent Sweeping Processes

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Abstract

In this paper, we study the existence of solutions for a time and state-dependent discontinuous nonconvex second order sweeping process with a multivalued perturbation. The moving set is assumed to be prox-regular, relatively ball-compact with a bounded variation. The perturbation of the normal cone is a scalarly upper semicontinuous convex valued multimapping satisfying a linear growth condition possibly time-dependent. As an application of the theoretical results, we investigate the theory of evolution quasi-variational inequalities.

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Acknowledgements

The authors would like to thank the two anonymous reviewers for their valuable suggestions on earlier versions of this paper.

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  1. Laboratoire XLIM, Université de Limoges, 123 Avenue Albert Thomas, 87060, Limoges Cedex, France

    S. Adly & F. Nacry

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  1. S. Adly
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  2. F. Nacry
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Correspondence to S. Adly.

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Adly, S., Nacry, F. An Existence Result for Discontinuous Second-Order Nonconvex State-Dependent Sweeping Processes. Appl Math Optim 79, 515–546 (2019). https://doi.org/10.1007/s00245-017-9446-9

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