Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916108423921664 |
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| author | Pang, Yan Xie, Junping Zhang, Xingyong |
| author_facet | Pang, Yan Xie, Junping Zhang, Xingyong |
| contents | We investigate a generalized poly-Laplacian system with a parameter on weighted finite graph, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a $(p,q)$-Laplacian system with a parameter on weighted locally finite graphs. We utilize a critical points theorem built by Bonanno and Bisci [Bonanno, Bisci, and Regan, Math. Comput. Model. 2010, 52(1-2): 152-160], which is an abstract critical points theorem without compactness condition, to obtain that these three systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs Pang, Yan Xie, Junping Zhang, Xingyong Analysis of PDEs We investigate a generalized poly-Laplacian system with a parameter on weighted finite graph, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a $(p,q)$-Laplacian system with a parameter on weighted locally finite graphs. We utilize a critical points theorem built by Bonanno and Bisci [Bonanno, Bisci, and Regan, Math. Comput. Model. 2010, 52(1-2): 152-160], which is an abstract critical points theorem without compactness condition, to obtain that these three systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range. |
| title | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.15372 |