Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914701187743744 |
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| author | Zhang, Xuechen Zhang, Xingyong |
| author_facet | Zhang, Xuechen Zhang, Xingyong |
| contents | We investigate the existence of ground state solutions for a $(p,q)$-Laplacian system with $p,q>1$ and potential wells on a weighted locally finite graph $G=(V,E)$. By making use of the method of Nehari manifold and the Lagrange multiplier rule, we prove that if the nonlinear term $F$ takes on the super-$(p, q)$-linear growth and the potential functions $a(x)$ and $b(x)$ satisfy some suitable conditions, then for any fixed parameter $λ\geq1$, the system is provided with a ground state solution $(u_λ, v_λ)$. Additionally, we set up the convergence property of the solutions set $\{(u_λ, v_λ)\}$ when $λ\rightarrow +\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs Zhang, Xuechen Zhang, Xingyong Analysis of PDEs We investigate the existence of ground state solutions for a $(p,q)$-Laplacian system with $p,q>1$ and potential wells on a weighted locally finite graph $G=(V,E)$. By making use of the method of Nehari manifold and the Lagrange multiplier rule, we prove that if the nonlinear term $F$ takes on the super-$(p, q)$-linear growth and the potential functions $a(x)$ and $b(x)$ satisfy some suitable conditions, then for any fixed parameter $λ\geq1$, the system is provided with a ground state solution $(u_λ, v_λ)$. Additionally, we set up the convergence property of the solutions set $\{(u_λ, v_λ)\}$ when $λ\rightarrow +\infty$. |
| title | Existence and convergence of ground state solutions for a $(p,q)$-Laplacian system on weighted graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.02048 |