In this paper, we study the existence and multiplicity of nontrivial solutions of a second-order discrete boundary value problem with resonance and sublinear or superlinear nonlinearity. The main methods are based on the Morse theory and the minimax methods. In addition, some examples are given to illustrate our results.

中文翻译：

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具有共振的二阶差分方程的边值问题

在本文中，我们研究了具有共振和亚线性或超线性非线性的二阶离散边值问题非平凡解的存在性和多重性。主要方法基于莫尔斯理论和极小极大方法。此外，还提供了一些示例来说明我们的结果。