p-Laplacian equations with general Choquard nonlinearity on lattice graphs

Abstract

In this paper, we study the following $p$-Laplacian equation $$-{\Delta }_{p}u+h(x)|u{|}^{p-2}u=\left(R_{\alpha }\ast F(u)\right)f(u)$$ on lattice graphs ${\mathbb{Z}}^N$, where $p\ge 2$, $\alpha \in (0,N)$ are constants and $R_{\alpha }$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under different assumptions on potential function $h$, we prove the existence of ground state solutions respectively by the methods of Nehari manifold.

arXiv comment14 pages