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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2025-04-01
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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. |
| format | Article |
| id | doaj-art-b6fce98d628b4938a26d5b18874e3abb |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| 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 |