Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs
Abstract We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a ( p , q ) $(p,q)$ -Laplacian system with a parameter on weighted locally...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01846-2 |
| _version_ | 1797233458659983360 |
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| author | Yan Pang Junping Xie Xingyong Zhang |
| author_facet | Yan Pang Junping Xie Xingyong Zhang |
| author_sort | Yan Pang |
| collection | DOAJ |
| description | Abstract We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a ( p , q ) $(p,q)$ -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. 52(1-2):152–160, 2010], which is an abstract critical points theorem without compactness condition, to obtain that these systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range. |
| first_indexed | 2024-04-24T16:16:30Z |
| format | Article |
| id | doaj.art-609a5962c1b3429fbc5c36c5a8b6d5a0 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-24T16:16:30Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-609a5962c1b3429fbc5c36c5a8b6d5a02024-03-31T11:27:06ZengSpringerOpenBoundary Value Problems1687-27702024-03-012024112310.1186/s13661-024-01846-2Infinitely many solutions for three quasilinear Laplacian systems on weighted graphsYan Pang0Junping Xie1Xingyong Zhang2Faculty of Science, Kunming University of Science and TechnologyFaculty of Transportation Engineering, Kunming University of Science and TechnologyFaculty of Science, Kunming University of Science and TechnologyAbstract We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a ( p , q ) $(p,q)$ -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. 52(1-2):152–160, 2010], which is an abstract critical points theorem without compactness condition, to obtain that these systems have infinitely many nontrivial solutions with unbounded norm when the parameters locate some well-determined range.https://doi.org/10.1186/s13661-024-01846-2Infinitely many solutionsGeneralized ploy-Laplacian system( p , q ) $(p,q)$ -Laplacian systemFinite graphLocally finite graph |
| spellingShingle | Yan Pang Junping Xie Xingyong Zhang Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs Boundary Value Problems Infinitely many solutions Generalized ploy-Laplacian system ( p , q ) $(p,q)$ -Laplacian system Finite graph Locally finite graph |
| title | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| title_full | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| title_fullStr | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| title_full_unstemmed | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| title_short | Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs |
| title_sort | infinitely many solutions for three quasilinear laplacian systems on weighted graphs |
| topic | Infinitely many solutions Generalized ploy-Laplacian system ( p , q ) $(p,q)$ -Laplacian system Finite graph Locally finite graph |
| url | https://doi.org/10.1186/s13661-024-01846-2 |
| work_keys_str_mv | AT yanpang infinitelymanysolutionsforthreequasilinearlaplaciansystemsonweightedgraphs AT junpingxie infinitelymanysolutionsforthreequasilinearlaplaciansystemsonweightedgraphs AT xingyongzhang infinitelymanysolutionsforthreequasilinearlaplaciansystemsonweightedgraphs |