Abstract
In this paper, we study a differential inclusion known as second-order sweeping process for a class of prox-regular non-convex sets. Assuming that such sets depend continuously on time and state, we give a new proof of the existence of solutions via Schauder’s fixed point theorem and the well-posedness for the perturbed first-order sweeping process in Hilbert spaces.
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The authors would like to acknowledge the referees for their careful reading and insightful suggestions.
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Lounis, S., Haddad , T. & Sene, M. Non-convex second-order Moreau’s sweeping processes in Hilbert spaces. J. Fixed Point Theory Appl. 19, 2895–2908 (2017). https://doi.org/10.1007/s11784-017-0461-x
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DOI: https://doi.org/10.1007/s11784-017-0461-x