BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator

Charles Castaing (), Christiane Godet-Thobie () and Manuel D. P. Monteiro Marques
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Charles Castaing: Institut Montpelliérian Alexander Grothendieck, Université de Montpellier II, CEDEX 5, 34095 Montpellier, France
Christiane Godet-Thobie: Laboratoire de Mathématiques de Bretagne Atlantique, Université de Brest, CNRS, UMR 6205, 6, Avenue Victor Le Gorgeu, CS 9387, CEDEX 3, 29238 Brest, France
Manuel D. P. Monteiro Marques: CMAFc10, Departemento de Matematica, Faculdade de Ciencias de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

Mathematics, 2024, vol. 12, issue 6, 1-44

Abstract: This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel.

Keywords: bounded variation; differential inclusion; maximal monotone operator; pseudo-distance; right continuous; second order; fractional derivative; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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