中文摘要：

研究具有次线性增长条件的二阶微分方程。由Gronwall不等式，得到解是全局存在的；利用解的弹性性质得到周期解的先验界；用度理论的延拓定理，得到了周期解存在的充分条件。

英文摘要：

Second order differential equation with sub-linear growth is investigated. Global existence of solution is proved by Gronwall inequity. Based on the ＂elastic property＂ of solutions, the priori estimate of the periodic solu- tions is given. A sufficient condition for existence of periodic solution is obtained by using continuation theorem of topological degree.