Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity

In this paper, we study the following Kirchhoff-Choquard equation $$-(a+b{\int }_{{\mathbb{Z}}^3}\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{2}d\mu )\mathrm{\Delta }u+h(x)u=(R_{\alpha }\ast \mathrm{\mid }u{\mathrm{\mid }}^p)\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u,x\in {\mathbb{Z}}^3,$$ where $a,b>0$, $\alpha \in (0,3)$ are constants and $R_{\alpha }$ is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on potential function $h$, for $p>2$, we first establish the existence of ground state solutions based on the Nehari manifold. Subsequently, for $p>4$, we obtain the existence of ground state sign-changing solutions by adopting constrained minimization arguments on the sign-changing Nehari manifold.