Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 634–650 | Cite as

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

  • Chems Eddine Arroud
  • Tahar HaddadEmail author


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.


Sweeping process Upper semicontinuous set-valued mapping Differential inclusion Subdifferential 

Mathematics Subject Classification

34A60 434K05 47J22 49J52 



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


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Authors and Affiliations

  1. 1.Laboratoire LMPEAUniversité de JijelJijelAlgeria

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