Multiple Solutions for Partial Discrete Dirichlet boundary value problem with p-Laplacian ltilltiftilitiiltllit-li

Abstract

By employing three critical points theorem, we investigate the existence of solutions to a boundary value problem for p-Laplacian partial difference equation with real parameter and give it accurate estimates to ensure that the studied problem has at least three solutions. Moreover, two positive solutions are obtained under some suitable assumptions for nonlinearity f depending on the strong maximum principle.