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<p>This study investigates a discrete Dirichlet problem governed by the singular nabla <i>ψ</i>-Laplacian operator. By utilizing a variational framework within a three critical points theorem, sufficient conditions are established to ensure the existence of multiple positive solutions. Specifically, we obtain the existence of at least three distinct solutions and identify parameter intervals, together with uniform bounds on their norms. Finally, the theoretical contributions are substantiated through a concrete numerical example, complete with visual representations that illustrate the geometry of the energy functional and confirm the multiplicity of the solutions.</p>

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Three distinct critical points for discrete Dirichlet problems governed by singular Laplacian

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月2日

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  • Meraa Arab,
  • Pshtiwan Othman Mohammed

摘要

This study investigates a discrete Dirichlet problem governed by the singular nabla ψ-Laplacian operator. By utilizing a variational framework within a three critical points theorem, sufficient conditions are established to ensure the existence of multiple positive solutions. Specifically, we obtain the existence of at least three distinct solutions and identify parameter intervals, together with uniform bounds on their norms. Finally, the theoretical contributions are substantiated through a concrete numerical example, complete with visual representations that illustrate the geometry of the energy functional and confirm the multiplicity of the solutions.