By applying variational arguments and the lower and upper solution method, we obtain several criteria for the existence of positive solutions to a class of singular discrete Dirichlet problems with a parameter. Our results cover the cases when the nonlinear function in the equation is superlinear, asymptotically linear, and sublinear. We provide several examples to illustrate our results.

中文翻译：

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一类带参数的奇异离散Dirichlet问题的正解

通过应用变分参数和上下求解方法，我们获得了带有参数的一类奇异离散Dirichlet问题正解存在性的若干标准。我们的结果涵盖了方程中的非线性函数为超线性，渐近线性和次线性的情况。我们提供了一些示例来说明我们的结果。