完全2n阶常微分方程的奇周期解  

Odd periodic solutions of fully 2nth-order ordinary differential equations

作　　者：李永祥 郭兰珺 LI Yong-xiang;GUO Lan-jun(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1期5-8,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11661071;11261053)

摘　　要：讨论完全2n阶常微分方程u(2n)(t)=f(t,u(t),u′(t),…,u(2n-1)(t))奇周期解的存在性与唯一性,其中n是正整数,f:R×R^(2n)→R连续且关于t以2π为周期.应用Fourier分析法和Leray-Schauder不动点定理,在非线性项f满足适当增长的条件下,获得了该方程奇2π周期解的存在性与唯一性.The existence and uniqueness of odd periodic solutions are discussed for fully nonlinear2nth-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 and2π-periodic with respect to t.By applying the Fourier analysis method and Leray-Schauder fixed point theorem,the results of existence and uniqueness of odd2π-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 

分 类 号：O175.8[理学—数学]