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A Weak Solution for a Nonlinear Fourth-Order Elliptic System with Variable Exponent Operators and Hardy Potential

Author

Listed:
  • Khaled Kefi

    (Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia)

  • Mohamad M. Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, we investigate the existence of at least one weak solution for a nonlinear fourth-order elliptic system involving variable exponent biharmonic and Laplacian operators. The problem is set in a bounded domain D ⊂ R N ( N ≥ 3 ) with homogeneous Dirichlet boundary conditions. A key feature of the system is the presence of a Hardy-type singular term with a variable exponent, where δ ( x ) represents the distance from x to the boundary ∂ D . By employing a critical point theorem in the framework of variable exponent Sobolev spaces, we establish the existence of a weak solution whose norm vanishes at zero.

Suggested Citation

  • Khaled Kefi & Mohamad M. Al-Shomrani, 2025. "A Weak Solution for a Nonlinear Fourth-Order Elliptic System with Variable Exponent Operators and Hardy Potential," Mathematics, MDPI, vol. 13(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1443-:d:1644714
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    References listed on IDEAS

    as
    1. Khaled Kefi & Mohammed M. Al-Shomrani, 2025. "Multiple Solutions for Double-Phase Elliptic Problem with NonLocal Interaction," Mathematics, MDPI, vol. 13(8), pages 1-12, April.
    2. 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.
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