This work is to discuss the Dirichlet boundary value problem of the difference equation with  -mean curvature operator. Under some determinate growth conditions on the nonlinear term, the existence of one solution or two nontrivial solutions is obtained via variational methods and some analysis techniques. Examples are also given to illustrate our theorems in the last section.

中文翻译：

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含平均曲率算子的离散Dirichlet问题解的存在性

这项工作是要讨论带有 -mean曲率算子的差分方程的Dirichlet边值问题。在某些确定的非线性条件下的增长条件下，通过变分方法和一些分析技术获得一个解或两个非平凡解的存在。最后一部分还给出了一些例子来说明我们的定理。