Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910407523827712 |
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| author | Yu, Zhangyi Xie, Junping Zhang, Xingyong Qi, Wanting |
| author_facet | Yu, Zhangyi Xie, Junping Zhang, Xingyong Qi, Wanting |
| contents | We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the variational methods which are based on mountain pass theorem and topological degree theory. We obtain that these two systems have a sequence of minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional $φ(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional $φ(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs Yu, Zhangyi Xie, Junping Zhang, Xingyong Qi, Wanting Analysis of PDEs We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the variational methods which are based on mountain pass theorem and topological degree theory. We obtain that these two systems have a sequence of minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional $φ(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional $φ(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$. |
| title | Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.08272 |