The positive solution for the nonlinear p-Laplacian Choquard equation on lattice graphs

In this paper, the author considers the nonlinear p-Laplacian Choquard equation on a weighted lattice graph. Under some suitable conditions on the potential function, the author proves that if the nonlinearity satisfies some growth conditions, the equation under study has a strictly positive solution. Compared with previous results, the conditions on the potential are relaxed and p can take any value in (1,+infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1,+\infty )$$\end{document}. Moreover, to our knowledge, there is currently no existence result for the p-Laplacian Choquard equation with the nonlinearity on lattice graphs.