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中文摘要：
基于近几十年发展起来的粘性解理论和传统的上、下解方法，作者考虑了一阶隐式微分方程的周期解问题．通过以粘性周期上、下解代替古典意义下的周期上、下解，作者证明了周期的Lipschitz粘性解的存在性，一方面减弱了已有文献中的相关条件，另一方面得到的解具有更好的正则性．
英文摘要：
This paper is concerned with periodic problem of first-order implicit differential equations. By substituting the periodic viscosity upper-lower solutions for the classical periodic upper-lower solutions, the existence of periodic viscosity solutions which are Lipschitz is proved. On one hand, these results improve the corresponding ones in the literature in the way that they weaken the conditions in the literature. The approach here is mainly based on the viscosity solution theory developed in recent decades and the classical upper-lower solutions method.
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