完全非线性三阶微分方程周期解的存在性

Existence of Periodic Solutions for Fully Third-order Nonlinear Ordinary Differential Equation

借助Fourier分析的方法及非线性项的扰动技巧,利用Leray-Schauder不动点定理,获得了完全非线性三阶微分方程u'''(t)=f(t,u(t),u′(t),u″(t)),t∈Rω-周期解的存在性及唯一性,其中f:R×R×R×R→R连续,关于t以ω为周期.

With the aid of the method of Fourier analysis and the perturbation technique of nonlinear term,the existence and uniqueness of ω-periodic solutions for the following fully third-order nonlinear ordinary differential equation is obtained by Leray-Schauder fixed point theorem,u（＂＇）（t） =f（t,u（t）,u＇ （t）,u＂（t））,t ∈ R,where f：R × R × R × R→R is a continuous function and is ω-periodic in t.