In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.

中文翻译：

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具有周期系数的二阶非线性泛函差分方程的多重变号解的存在性

在本文中，我们应用下降流不变集的方法来建立一系列准则，以确保具有周期性边界条件的二阶非线性函数差分方程至少具有一个平凡解和三个非平凡解。这些非平凡解由符号变化解、正解和负解组成。此外，作为我们理论结果的应用，详细说明了一个例子。我们的结果概括并改进了一些现有的结果。