一类三阶非线性微分方程的奇周期解

Odd periodic solutions for three order ordinary differential equations

本文考虑三阶微分方程u′′′(t)=f t,u (t),u′(t))奇周期解的存在性,其中f:R×R^2→R为连续的奇函数,f t(,u,v)关于t以2π为周期.在一个使f t(,u,v)关于u与v超线性增长的条件下,本文利用Leray-Schauder不动点定理得出奇2π周期解的存在唯一性.

This paper deals with the existence of odd periodic solutions for three order ordinary differential equation u′′′（t）=f t,u （t）,u′（t）） , where f：R×R2→R is a continuous odd function and f（t,u,v） is 2π -periodic in t. Under a condition allowing that f（t,u,v） is superlinear in u and v , we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.