Infinitely Many Solutions for Discrete Boundary Value Problems with the p , q -Laplacian Operator

Abstract

In this paper, we consider the existence and multiplicity of solutions for a discrete Dirichlet boundary value problem involving the $\left(p,q\right)$ -Laplacian. By using the critical point theory, we obtain the existence of infinitely many solutions under some suitable assumptions on the nonlinear term. Also, by our strong maximum principle, we can obtain the existence of infinitely many positive solutions.