This paper deals with the existence and uniqueness of solutions for 2nth‐order ordinary differential equation with periodic boundary value condition u(2n) (t)+ au(t) = f (t ,u(t) ,u′(t) ,… ,u(2n-1) (t)) , t ∈ I , u(i) (0) = u(i) (2π) , i = 0 ,1 ,… ,2n-1 . Where n≥1 is a integer , I= [0 ,2π] ,(-1)n a>0 ,f :I × R2n R is continuous and 2π‐peridoic with respect to t . By applying the Fourier analysis method and Leray‐Schauder fixed point theorem , the results of existence and uniqueness are obtained w hen the nonlinearity f satisifies proper grow th conditions .%研究2n阶非线性常微分方程周期边值问题u(2 n)( t)+ au ( t)= f ( t ,u( t),u′( t),…,u(2 n-1)( t)), t ∈ I , u(i)(0)= u(i)(2π), i =0,1,…,2n-1解的存在唯一性,其中 n≥1是整数, I=[0,2π],(-1)n a>0,f :I × R2n R连续且关于 t以2π为周期。运用Fourier分析法和Leray‐Schauder不动点定理,获得了当非线性项 f满足适当增长条件时,该问题解的存在唯一性结果。
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