Weak Solutions to Leray–Lions-Type Degenerate Quasilinear Elliptic Equations with Nonlocal Effects, Double Hardy Terms, and Variable Exponents

Khaled Kefi () and Mohammed M. Al-Shomrani
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Khaled Kefi: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
Mohammed M. Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2025, vol. 13, issue 7, 1-14

Abstract: This study investigates the existence and multiplicity of weak solutions for a class of degenerate weighted quasilinear elliptic equations that incorporate nonlocal nonlinearities, a double Hardy term, and variable exponents. The problem encompasses a degenerate nonlinear operator characterized by variable exponent growth, along with a nonlocal interaction term and specific constraints on the nonlinearity. By employing critical point theory, we establish the existence of at least three weak solutions under sufficiently general assumptions.

Keywords: variational methods; Hardy inequality; degenerate Leray–Lions p ( x )-Laplacian operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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