In this paper, the existence and uniqueness of response solutions, which has the same frequency with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the -property of quasiperiodic functions.

中文翻译：

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带有参数反射的奇摄动系统的响应解

在本文中，研究了带有参数反射的拟周期奇摄动系统的响应解的存在性和唯一性，该响应解具有与非线性项相同的频率。首先，我们证明所有具有频率的拟周期函数都形成一个Banach空间。然后，通过定点方法和拟周期函数的-性质，获得了拟周期解的存在性和唯一性。