Abstract

This paper is devoted to weaken "classical" assumptions and to give new arguments to prove existence of solutions of differential inclusions with proximal normal cones in Banach spaces. Mainly we define the concept of "directional prox-regularity" and give assumptions on a Banach space to ensure the existence of such differential inclusions (which permits to generalize existing results requiring a Hilbertian structure).

Author information

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Keywords

  • Differential inclusion
  • sweeping process
  • prox-regularity
  • proximal normal cone

Mathematics Subject Classification

34A60, 49J52, 58C20

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Suggested citation

F. Bernicot, J. Venel. “Differential Inclusions with Proximal Normal Cones in Banach Spaces.” Journal of Convex Analysis 17 (2010), No. 2, 451–484. https://doi.org/10.68381/jca17032

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.