Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909708884901888 |
|---|---|
| author | Wang, Lidan |
| author_facet | Wang, Lidan |
| contents | In this paper, we study the $p$-Laplacian system with Choquard-type nonlinearity $$ \begin{cases}-Δ_{p} u+(λa+1)|u|^{p-2} u=\frac{1}γ \left(R_α\ast F(u,v)\right)F_{u}(u, v), \\ -Δ_{p} v+(λb+1)|v|^{p-2} v=\frac{1}γ \left(R_α\ast F(u,v)\right)F_{v}(u, v),\end{cases} $$ on lattice graphs $\mathbb{Z}^N$, where $α\in(0,N),\,p\geq 2,\,γ> \frac{(N+α)p}{2N},\,λ>0$ is a parameter and $R_α$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some assumptions on the functions $a,\,b$ and $F$, we prove the existence and asymptotic behavior of ground state solutions by the method of Nehari manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs Wang, Lidan Analysis of PDEs 35J92, 35J50, 35R02 In this paper, we study the $p$-Laplacian system with Choquard-type nonlinearity $$ \begin{cases}-Δ_{p} u+(λa+1)|u|^{p-2} u=\frac{1}γ \left(R_α\ast F(u,v)\right)F_{u}(u, v), \\ -Δ_{p} v+(λb+1)|v|^{p-2} v=\frac{1}γ \left(R_α\ast F(u,v)\right)F_{v}(u, v),\end{cases} $$ on lattice graphs $\mathbb{Z}^N$, where $α\in(0,N),\,p\geq 2,\,γ> \frac{(N+α)p}{2N},\,λ>0$ is a parameter and $R_α$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some assumptions on the functions $a,\,b$ and $F$, we prove the existence and asymptotic behavior of ground state solutions by the method of Nehari manifold. |
| title | Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs |
| topic | Analysis of PDEs 35J92, 35J50, 35R02 |
| url | https://arxiv.org/abs/2507.20464 |