Positive solutions of the discrete Dirichlet problem involving the mean curvature operator. (English) Zbl 1426.39023
Summary: 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.
MSC:
| 39A70 | Difference operators |
| 39A21 | Oscillation theory for difference equations |
| 39A12 | Discrete version of topics in analysis |
Keywords:
discrete Dirichlet problem; mean curvature operator; infinitely many positive solutions; critical point theoryReferences:
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