The existence of periodic solution to nonlinear functional difference equation is considered by using the topological degree, and a periodic solution of this problem is obtained.

利用拓扑度理论对一类非线性泛函差分方程周期解的存在性进行了讨论，得到该问题周期解的一个存在定理。

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Applying the theory of integral equation and functional analysis, we prove the existence and uniqueness of the system solution to the equation, and get the analytical expression of the solution.

运用泛函分析和积分方程理论，证明了系统解的存在性与唯一性，得到系统解的解析表达式。

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