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<p>The objective of this paper is to investigate the existence of positive solutions to the discrete <i>p</i>-Laplacian boundary value problem of Kirchhoff-type by means of the critical point theory. It is demonstrated that the problem possesses at least three solutions or at least two solutions under distinct assumptions regarding the nonlinear term <i>f</i>. We establish a strong maximum principle for the problem and obtain the existence and multiplicity of positive solutions. When we apply our theorems to the classical problem of Kirchhoff-type, we obtain new conditions for the existence of three positive solutions. Finally, we take three examples to verify our results.</p>

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Positive Solutions to the Discrete p-Laplacian Boundary Value Problem of Kirchhoff-Type

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Zhi Chen,
  • Zhan Zhou

摘要

The objective of this paper is to investigate the existence of positive solutions to the discrete p-Laplacian boundary value problem of Kirchhoff-type by means of the critical point theory. It is demonstrated that the problem possesses at least three solutions or at least two solutions under distinct assumptions regarding the nonlinear term f. We establish a strong maximum principle for the problem and obtain the existence and multiplicity of positive solutions. When we apply our theorems to the classical problem of Kirchhoff-type, we obtain new conditions for the existence of three positive solutions. Finally, we take three examples to verify our results.