Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian

The aim of this paper is to investigate the existence of positive solutions for a discrete Robin problem of the Kirchhoff type involving the <i>p</i>-Laplacian by the means of critical point theory. Our results demonstrate that the problem admits at least three solutions, or at least two...

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Main Authors: Zhi Chen, Zhan Zhou
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/4/285
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author Zhi Chen
Zhan Zhou
author_facet Zhi Chen
Zhan Zhou
author_sort Zhi Chen
collection DOAJ
description The aim of this paper is to investigate the existence of positive solutions for a discrete Robin problem of the Kirchhoff type involving the <i>p</i>-Laplacian by the means of critical point theory. Our results demonstrate that the problem admits at least three solutions, or at least two solutions under different conditions on the nonlinear term <i>f</i>. We establish a strong maximum principle for the problem and obtain the existence and multiplicity of positive solutions. Finally, we give three examples to verify our results.
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spelling doaj-art-b6fce98d628b4938a26d5b18874e3abb2025-08-20T03:14:25ZengMDPI AGAxioms2075-16802025-04-0114428510.3390/axioms14040285Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-LaplacianZhi Chen0Zhan Zhou1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaThe aim of this paper is to investigate the existence of positive solutions for a discrete Robin problem of the Kirchhoff type involving the <i>p</i>-Laplacian by the means of critical point theory. Our results demonstrate that the problem admits at least three solutions, or at least two solutions under different conditions on the nonlinear term <i>f</i>. We establish a strong maximum principle for the problem and obtain the existence and multiplicity of positive solutions. Finally, we give three examples to verify our results.https://www.mdpi.com/2075-1680/14/4/285p-Laplaciandiscrete Robin problempositive solutionscritical point theorystrong maximum principle
spellingShingle Zhi Chen
Zhan Zhou
Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
Axioms
p-Laplacian
discrete Robin problem
positive solutions
critical point theory
strong maximum principle
title Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
title_full Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
title_fullStr Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
title_full_unstemmed Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
title_short Positive Solutions for Discrete Robin Problem of Kirchhoff Type Involving <i>p</i>-Laplacian
title_sort positive solutions for discrete robin problem of kirchhoff type involving i p i laplacian
topic p-Laplacian
discrete Robin problem
positive solutions
critical point theory
strong maximum principle
url https://www.mdpi.com/2075-1680/14/4/285
work_keys_str_mv AT zhichen positivesolutionsfordiscreterobinproblemofkirchhofftypeinvolvingipilaplacian
AT zhanzhou positivesolutionsfordiscreterobinproblemofkirchhofftypeinvolvingipilaplacian