On a class of evolution problems driven by  maximal monotone operators with integral perturbation

Fatima Fennour; Soumia Saïdi

doi:10.56754/0719-0646.2601.123

DOI:

https://doi.org/10.56754/0719-0646.2601.123

Abstract

The present paper is dedicated to the study of a first-order differential inclusion driven by time and state-dependent maximal monotone operators with integral perturbation, in the context of Hilbert spaces. Based on a fixed point method, we derive a new existence theorem for this class of differential inclusions. Then, we investigate an optimal control problem subject to such a class, by considering control maps acting in the state of the operators and the integral perturbation.

Keywords

Integro-differential inclusion , maximal monotone operator , integral perturbation , optimal solution

Mathematics Subject Classification:

34A60 , 34G25 , 47H10 , 47J35 , 49J52 , 49J53 , 45J05

Fatima Fennour LMPA Laboratory, Department of Mathematics, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria. https://orcid.org/0009-0003-4004-7305
Soumia Saïdi LMPA Laboratory, Department of Mathematics, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria. https://orcid.org/0000-0002-4242-8940

Pages: 123–151
Date Published: 2024-04-09
Vol. 26 No. 1 (2024)

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