In this paper, we consider an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of $\ddot{x}+x=0$ under piecewise smooth perturbation. By using the first order average method, we prove that the maximum number is at most n and n can be reached.

中文翻译：

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分段光滑微分系统的最大极限环数

在本文中，我们考虑了由的周期解产生的最大极限环数的一个上限。 $\ddot{X}+X=0$在分段平滑扰动下。通过使用一阶平均法，我们证明最大数最多为n，并且可以达到n。