SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2476-2490, January 2021.
Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of the Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth differential equations, there is a huge class of differential equations lacking in a higher order analysis on the existence of periodic solutions, namely, the class of continuous non-Lipschitz differential equations. In this paper, based on the degree theory for operator equations, we perform a higher order analysis of continuous perturbed differential equations and derive sufficient conditions for the existence and uniform convergence of periodic solutions for such systems. We apply our results to study continuous non-Lipschitz higher order perturbations of a harmonic oscillator.

中文翻译：

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基于度理论的连续微分方程周期解存在性的高阶分析

SIAM数学分析杂志，第53卷，第2期，第2476-2490页，2021年1月。
最近，根据布劳维尔度数理论，开发了用于研究Lipschitz微分方程和不连续分段光滑微分方程的周期解的高阶平均方法。在Lipschitz和不连续的分段光滑微分方程之间，存在一类极大的微分方程，缺乏关于周期解存在性的高阶分析，即一类连续的非Lipschitz微分方程。在本文中，基于算子方程的度理论，我们对连续扰动微分方程进行了更高阶的分析，并为此类系统的周期解的存在和一致收敛导出了充分的条件。