The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth

Ruowei Li, Lidan Wang

In this paper, we study the nonlinear Choquard equation \begin{eqnarray*} Δ^{2}u-Δu+(1+λa(x))u=(R_α\ast|u|^{p})|u|^{p-2}u \end{eqnarray*} on a Cayley graph of a discrete group of p…