We analyze the nondegeneracy of second-order linear neutral differential equation

$$\begin{aligned} (x(t)-cx(t-\tau ))''=a(t)x(t), \end{aligned}$$

where c is a constant. By applications of the nondegeneracy of this linear neutral equation and an extension of Mawhin’s continuation theorem, we obtain existence and uniqueness of periodic solution for the prescribed second-order neutral differential equations. At last, we give two examples to show the applications of the theorems.

中文翻译：

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中立型微分方程周期解的非退化性和唯一性。

我们分析了二阶线性中立型微分方程的非退化性

$$ \ begin {aligned}（x（t）-cx（t- \ tau））''= a（t）x（t），\ end {aligned} $$

其中c是常数。通过应用该线性中立方程的非退化性和Mawhin连续定理的扩展，我们得到了所规定的二阶中立型微分方程周期解的存在性和唯一性。最后，我们给出两个例子来说明定理的应用。