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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Khaled Kefi & Mohammed M. Al-Shomrani, 2025. "Weak Solutions to Leray–Lions-Type Degenerate Quasilinear Elliptic Equations with Nonlocal Effects, Double Hardy Terms, and Variable Exponents," Mathematics, MDPI, vol. 13(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1185-:d:1627652
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