We consider third-order autonomous continuous piecewise differential equations in the variable [Formula: see text]. For such differential equations with nonlinearities of the form [Formula: see text], we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class [Formula: see text].

中文翻译：

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具有分段多项式非线性的连续三阶微分方程的周期解

我们考虑变量中的三阶自主连续分段微分方程[公式：见正文]。对于具有[公式：见文本]形式的非线性微分方程，我们使用平均理论研究它们的周期解。我们注意到，由于微分系统只是连续的，我们不能将经典的平均理论应用于它，这需要微分系统至少属于类 [公式：见文本]。