Abstract
This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form −Du∈N C (t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ℝd,N C(t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]×ℝd→ℝd is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.
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Castaing, C., Marques, M.D.P.M. BV periodic solutions of an evolution problem associated with continuous moving convex sets. Set-Valued Anal 3, 381–399 (1995). https://doi.org/10.1007/BF01026248
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DOI: https://doi.org/10.1007/BF01026248