Existence of weak solutions for a class of (p(u),q(u))-Laplacian problems

Youssef Fadil; Said Ait  Temghart; Chakir Allalou; Mohamed Oukessou

doi:10.56947/gjom.v17i1.2098

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Published: Jul 10, 2024

DOI: https://doi.org/10.56947/gjom.v17i1.2098

Keywords:

Laplacian, elliptic problems, variable nonlinearity, generalized Sobolev spaces

Youssef Fadil

Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Techniques, Sultan Moulay Silmane University, Beni Mellal, Morocco

Said Ait Temghart

Laboratory of Computer Systems Engineering, Mathematics and Applications, Ibn Zohr University, Agadir, Morocco

Chakir Allalou

Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Techniques, Sultan Moulay Silmane University, Beni Mellal, Morocco

Mohamed Oukessou

Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Techniques, Sultan Moulay Silmane University, Beni Mellal, Morocco

Abstract

This paper investigates the existence of weak solutions for (p,q)-Laplacian problems where p and q depend on the unknown solution. We focus on the case where p and q are local quantities. By means of a singular perturbation technique, we prove the existence of weak solutions for certain Dirichlet problem.

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How to Cite

Fadil, Y., Temghart, S. A., Allalou, C., & Oukessou, M. (2024). Existence of weak solutions for a class of (p(u),q(u))-Laplacian problems. Gulf Journal of Mathematics, 17(1), 261-274. https://doi.org/10.56947/gjom.v17i1.2098

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Vol. 17 No. 1 (2024)

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