关键词: 周期解, Schauder不动点定理, 存在性, 唯一性

Abstract:

The periodic solutions for second order differential equations were investigated by means of  the Schauder’s fixed point theorem. The existence and uniqueness of periodic solutions are established when the function f(t,x,x′) is continuously differentiable. Furthermore, under the condition that the right\|handfunction is only continuous, we have established the sufficient conditions for  the existence of periodic solutions.

Key words: periodic solutions, Schauder’s fixed point theorem, existence, uniqueness