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<p>Using variational methods and critical point theory, this paper investigates parameter intervals that guarantee the existence of at least three solutions for a new class of partially discrete Dirichlet boundary value problems involving the <i>ψ</i>-Laplacian. We also determine parameter regimes under which the norms of these solutions are bounded above by a prescribed positive constant. Furthermore, by employing the strong maximum principle, we show that under suitable assumptions the problem admits at least two and in certain cases three positive solutions. Finally, two illustrative examples are provided to substantiate the theoretical results.</p>

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Existence of three solutions for partial discrete Dirichlet boundary value problems containing ψ-Laplacian

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月5日

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  • Weimiao Zhou,
  • Genghong Lin,
  • Juping Ji

摘要

Using variational methods and critical point theory, this paper investigates parameter intervals that guarantee the existence of at least three solutions for a new class of partially discrete Dirichlet boundary value problems involving the ψ-Laplacian. We also determine parameter regimes under which the norms of these solutions are bounded above by a prescribed positive constant. Furthermore, by employing the strong maximum principle, we show that under suitable assumptions the problem admits at least two and in certain cases three positive solutions. Finally, two illustrative examples are provided to substantiate the theoretical results.