西北师范大学学报（自然科学版）2018，Vol.54Issue(1)：5-8,4.DOI:10.16783/j.cnki.nwnuz.2018.01.002
完全2n阶常微分方程的奇周期解
Odd periodic solutions of fully 2nth-order ordinary differential equations
摘要
Abstract
The existence and uniqueness of odd periodic solutions are discussed for fully nonlinear 2nth-order ordinary differential equations u(2n) (t) = f (t ,u(t) ,u′(t) ,… ,u(2n-1) (t)) , where n is a positive integer , f :R× R2n→ R is continuous and 2π-periodic with respect to t .By applying the Fourier analysis method and Leray-Schauder fixed point theorem , the results of existence and uniqueness of odd 2π-periodic solutions are obtained under the nonlinearity f satisfies proper growth conditions .关键词
2n常阶微分方程/奇周期解/Fourier级数展式/Leray-Schauder不动点定理Key words
2nth-order ordinary differential equation/odd periodic solution/Fourier series expansion/Leray-Schauder fixed point theorem分类
数理科学引用本文复制引用
李永祥,郭兰珺..完全2n阶常微分方程的奇周期解[J].西北师范大学学报（自然科学版）,2018,54(1):5-8,4.基金项目
国家自然科学基金资助项目(11661071 ,11261053 ) （11661071 ,11261053 ）
