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On Evolution Equations Having Hypomonotonicities of Opposite Sign Governed by Sweeping Processes

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Abstract

We prove the local existence of solutions of a sweeping process involving a locally prox-regular set of constraints with an upper semicontinuous set-valued perturbation contained in the Clarke subdifferential of a nonconvex function. The study requires the quantified concept of local prox-regularity for the set of constraints. This paper can be considered as an improvement of previous works, since this existence (local) result is established without compactness condition on the set of constraints.

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Acknowledgements

The authors would like to acknowledge the referees for their careful reading and insightful suggestions.

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Authors and Affiliations

  1. Laboratoire LMPEA, Université de Jijel, 18000, Jijel, Algeria

    Chems Eddine Arroud & Tahar Haddad

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  1. Chems Eddine Arroud
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  2. Tahar Haddad
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Correspondence to Tahar Haddad.

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Communicated by Mimmo Iannelli.

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Arroud, C.E., Haddad, T. On Evolution Equations Having Hypomonotonicities of Opposite Sign Governed by Sweeping Processes. J Optim Theory Appl 180, 634–650 (2019). https://doi.org/10.1007/s10957-018-1423-1

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  • DOI: https://doi.org/10.1007/s10957-018-1423-1

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