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Research Article | Open Access

Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents

Khaled Kefi1( ), Nasser S. Albalawi2
Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
Department of Computer Sciences, Faculty of Computing and Information Technology, Northern Border University, Rafha, Saudi Arabia
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Abstract

This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations.

Keywords

variational methodsHardy inequalitydegenerate p(x)-Laplacian operators
CLC number: 35J15, 35J20, 35J25

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 4492-4503
DOI: 10.3934/math.2025207

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Cite this article:
Kefi K, Albalawi NS. Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents. AIMS Mathematics, 2025, 10(2): 4492-4503. https://doi.org/10.3934/math.2025207

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Received: 30 December 2024
Revised: 19 February 2025
Accepted: 25 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)