Positive solutions of the discrete Dirichlet problem involving the mean curvature operator

Abstract

In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the discrete Dirichlet problem involving the mean curvature operator. We show that the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. We also give two examples to illustrate our main results.

Keywords

• discrete dirichlet problem
• mean curvature operator
• infinitely many positive solutions
• critical point theory
• 39a11