二阶常微分方程拟周期解的存在性

Existence of the Quasi-periodic Solutions of Second Order Ordinary Differential Equations

研究了一类二阶常微分方程d2 udt2 +a1dudt+a2 u =f(t) ,a1,a2 都是常数 ,f(t)是周期为 2π的实值函数的拟周期解 ,通过使用Fourier分析方法和待定系数法 ,给出了这类方程拟周期性存在的充分性条件 .所用的方法对高阶、变系数常 (偏 )微分方程。

In this paper, quasi periodic solutions of a second order ordinary differential equations are considered and a sufficient condition about the existence of quasi periodic of the equations is obtained by means of Fourier series method and coefficient comparison. The method is rather general, which can be applied to many other equations.