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<p>We consider a class of discrete boundary value problems involving the <i>p</i>-Laplacian and prove, by confirming the parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> in an interval related to the first and last eigenvalues, the existence of at least three distinct solutions under hypotheses on nonlinearity. Further, we extend our results to demonstrate that the problem admits a sequence of pairwise distinct solutions for a specific range of parameters. Finally, we present two examples to confirm our results. Our approach is based on critical point theory.</p>

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Existence results for the second-order discrete boundary value problem involving the p-Laplacian with a parameter

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Anouar El-Allaly,
  • Omar Hammouti,
  • Mounir Mekkour

摘要

We consider a class of discrete boundary value problems involving the p-Laplacian and prove, by confirming the parameter \(\mu \) μ in an interval related to the first and last eigenvalues, the existence of at least three distinct solutions under hypotheses on nonlinearity. Further, we extend our results to demonstrate that the problem admits a sequence of pairwise distinct solutions for a specific range of parameters. Finally, we present two examples to confirm our results. Our approach is based on critical point theory.