| Abstract: |
| In this talk, we will introduce some results on the positive solutions for some nonlinear discrete Dirichlet boundary value problems involving the mean curvature operator by using critical point theory. Sufficient conditions on the existence of infinitely many positive solutions are given. 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. The existence of at least two positive solutions is also established when the nonlinear term is not oscillatory both at the origin and at infinity. Examples are given to illustrate our main results at last. |
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