中文摘要：

本文研究了具有扭转性的二阶微分方程,证明在一定条件下通过角函数的扭转所表述的几何性质可以得到周期解的存在性.从而得到了一些无先验界的时变位势的超线性二阶微分方程和可逆系统的周期解的存在性的新结果.

英文摘要：

We study some twist second order differential equations.We prove that in some cases,the geometric property of angle function implies the existence of periodic solutions.As the applications,we obtain some new results for the existence of periodic solutions for some second order equations or reversible systems without a priori bounds, such as superlinear second order equations or reversible systems with time-dependent potential.