Ground state solutions of $p$-Laplacian equations with nonnegative potentials on Lattice graphs

Xinrong Zhao

In this paper, we study the $p$-Laplacian equation $$-{\Delta }_{p}u+V(x)|u{|}^{p-2}u=f(x,u)$$ on the lattice graph ${\mathbb{Z}}^N$ with nonnegative potentials, where ${\Delta }_p$ is the discre…