The topological degree methods for the fractional \(p(\cdot)\)-Laplacian problems with discontinuous nonlinearities

Hasnae El Hammar; Chakir Allalou; Adil Abbassi; Abderrazak Kassidi

doi:10.4067/S0719-06462022000100063

DOI:

https://doi.org/10.4067/S0719-06462022000100063

Abstract

In this article, we use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional \(p(x)\)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent.

Keywords

Fractional p(x)-Laplacian , weak solution , discontinuous nonlinearity , topological degree theory

Hasnae El Hammar Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco.
Chakir Allalou Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco.
Adil Abbassi Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco.
Abderrazak Kassidi Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco.

Pages: 63–82
Date Published: 2022-04-04
Vol. 24 No. 1 (2022)

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