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Sweeping process with right uniformly lower semicontinuous mappings

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Abstract

In this paper, we establish, in the setting of infinite dimensional Hilbert space, a new existence result for nonconvex sweeping process with right uniformly lower semicontinuous sets. This class of sets is more general than the classical assumption of absolutely continuous sets, and contains hyperplanes and half-spaces. Further, we apply on the problem an unbounded set-valued perturbation and we state the existence of solution.

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Acknowledgements

The authors wish to thank the referees for careful reading of the paper and many valuable comments and remarks, which help to improve our presentation. We also thank Professor Lionel Thibault for his valuable comments and suggestions.

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Correspondence to Mustapha Fateh Yarou.

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Boudada, S., Yarou, M.F. Sweeping process with right uniformly lower semicontinuous mappings. Positivity 24, 207–228 (2020) doi:10.1007/s11117-019-00674-4

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Keywords

  • Proximal normal cone
  • Sweeping process
  • Perturbation
  • Prox-regular set
  • Uniformly lower semicontinuous from the right mapping

Mathematics Subject Classification

  • 34A60
  • 49J52
  • 28A25