Apartial discrete Dirichlet boundary value problem involving mean curvature operator is concerned in this paper. Under proper assumptions on the nonlinear term, we obtain some feasible conditions on the existence of multiple solutions by the method of critical point theory. We further separately determine open intervals of the parameter to attain at least two positive solutions and an unbounded sequence of positive solutions with the help of the maximum principle.

中文翻译：

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带平均曲率算子的偏离散Dirichlet边值问题多解的存在性

本文研究了涉及平均曲率算子的偏离散Dirichlet边值问题。在对非线性项进行适当假设的情况下，我们通过临界点理论的方法得到了多解存在的一些可行条件。我们进一步分别确定参数的开区间，以在最大值原理的帮助下获得至少两个正解和一个无界的正解序列。