关于二阶常微分方程周期解的定理

A THEOREM ON EXISTENCE OF PERIODIC SOLUTION FOR SECOND ORDER O.D.E.

本文研究非自治非线性二阶常微分方程存在周期解的充分条件．在满足本文定理的条件下，作者证明所研究的二阶方程在相空间中的Ｐｏｉｎｃａｒｅ映射是平面上有奇点的动力系统，从而证明原方程有周期解．这一结果全面推广已有的若干结论．

In this paper we study the sufficient conditions of existence of the periodic solution for the second order O.D.E.We prove that,under the theorem's conditions the Poincar6 mapping of the O.D.E.is the dynamical system on plane, which has at least a nontrivial singularityj hence the O.D.E.has nontrivial periodic solution. The result in this paper is generality of the preceding.