Solutions to discrete nonlinear Kirchhoff-Choquard equations

In this paper, we study the discrete Kirchhoff-Choquard equation -(a+b ∫Z³|∇ u|² d μ) Δ u+V(x) u=(Rα *F(u))f(u), x∈ Z³, where $a,\,b>0$ are constants, Rα is the Green's function of the discrete fractional Laplacian with α ∈(0,3), which has no singularity but has same asymptotics as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions by variational methods.