Three positive solutions for a nonlinear partial discrete Dirichlet problem with (p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}-Laplacian operator

In this paper, we prove the existence of three solutions to a partial difference equation with (p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}-Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinearity assumptions. Finally, we also give an example to illustrate our main results.