Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs

In this paper, we study the $p$-Laplacian system with Choquard-type nonlinearity $$\{\begin{array}{l}-{\mathrm{\Delta }}_{p}u+(\lambda a+1)\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u=\frac{1}{\gamma }(R_{\alpha }\ast F(u,v))F_u(u,v),\\ -{\mathrm{\Delta }}_{p}v+(\lambda b+1)\mathrm{\mid }v{\mathrm{\mid }}^{p-2}v=\frac{1}{\gamma }(R_{\alpha }\ast F(u,v))F_v(u,v),\end{array}$$ on lattice graphs ${\mathbb{Z}}^N$, where $\alpha \in (0,N),p\ge 2,\gamma >\frac{(N+\alpha )p}{2N},\lambda >0$ is a parameter and $R_{\alpha }$ 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.