p-Laplacian equations with general Choquard nonlinearity on lattice graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916362815799296 |
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| author | Wang, Lidan |
| author_facet | Wang, Lidan |
| contents | In this paper, we study the following $p$-Laplacian equation $$ -Δ_{p} u+h(x)|u|^{p-2} u=\left(R_α *F(u)\right)f(u) $$ on lattice graphs $\mathbb{Z}^N$, where $p\geq 2$, $α\in(0,N)$ are constants and $R_α$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under different assumptions on potential function $h$, we prove the existence of ground state solutions respectively by the methods of Nehari manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_10584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | p-Laplacian equations with general Choquard nonlinearity on lattice graphs Wang, Lidan Analysis of PDEs 35J20, 35J60, 35R02 In this paper, we study the following $p$-Laplacian equation $$ -Δ_{p} u+h(x)|u|^{p-2} u=\left(R_α *F(u)\right)f(u) $$ on lattice graphs $\mathbb{Z}^N$, where $p\geq 2$, $α\in(0,N)$ are constants and $R_α$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under different assumptions on potential function $h$, we prove the existence of ground state solutions respectively by the methods of Nehari manifold. |
| title | p-Laplacian equations with general Choquard nonlinearity on lattice graphs |
| topic | Analysis of PDEs 35J20, 35J60, 35R02 |
| url | https://arxiv.org/abs/2408.10584 |