Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity

In this paper, we study the following Kirchhoff-Choquard equation -(a+b ∫Z³|∇ u|² d μ) Δ u+h(x) u=(Rα|u|ᵖ)|u|ᵖ⁻²u, x∈ Z³, where $a,\,b>0$, α ∈(0,3) are constants and Rα 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.