p-Laplacian equations with general Choquard nonlinearity on lattice graphs

TL;DR

This paper investigates p-Laplacian equations with Choquard nonlinearity on lattice graphs, establishing the existence of ground state solutions using Nehari manifold methods under various potential conditions.

Contribution

It introduces new existence results for ground state solutions of p-Laplacian equations with Choquard nonlinearity on lattice graphs, employing Nehari manifold techniques.

Findings

Existence of ground state solutions under different potential assumptions

Application of Nehari manifold method to discrete fractional Laplacian equations

Extension of continuous models to lattice graph settings

Abstract

In this paper, we study the following $p$-Laplacian equation $$ -\Delta_{p} u+h(x)|u|^{p-2} u=\left(R_{\alpha} *F(u)\right)f(u) $$ on lattice graphs $\mathbb{Z}^N$, where $p\geq 2$, $\alpha \in(0,N)$ 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.