Abstract In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory. Several examples are provided to illustrate applications of our results.

中文翻译：

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基于莫尔斯理论的离散基尔霍夫型问题的非平凡解

摘要 在本文中，我们研究了非线性在零和无穷大处均共振时的离散基尔霍夫型问题。我们通过将变分方法与莫尔斯理论相结合，建立了一系列关于非平凡解存在性的结果。提供了几个例子来说明我们的结果的应用。