一类2n阶常微分方程的奇周期解  

Odd periodic solutions for a class of 2n order ordinary differential equations

作　　者：李永祥 文乾 LI Yong-xiang;WEN Qian(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2018年第4期1-4,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11261053;11661071)

摘　　要：讨论了2n阶常微分方程u^(2n)(t)=f(t,u(t),u″(t),…,u^(2n-2)(t)),t∈R奇2π-周期解的存在性,其中n是正整数,f:R×R^n—→R连续且关于t是以2π为周期的奇函数.运用Leray-Schauder不动点定理与Fourier分析方法,在允许非线性项f超线性增长的条件下,获得了该方程的奇2π-周期解.The existence of odd 2π-periodic solutions is discussed for nonlinear 2n th-order ordinary differential equations u （2n） （t）=f（t,u（t）,u″（t）,…,u （2n-2） （t））, t∈ R ,where n is a positive integer, f： R × R n R is continuous and odd 2π-periodic with respect to t .By applying the Leray-Schauder fixed point theorem and Fourier analysis method,the results of existence of odd 2π-periodic solutions is obtained under the nonlinearity f satisfies superlinear growth conditions.

关 键 词：超线性增长 奇周期解 LERAY-SCHAUDER不动点定理 FOURIER分析 

分 类 号：O177.91[理学—数学]