一类三阶非线性微分方程周期边值问题解的存在性  

Existence of solutions for a class of periodic bourdary value problem of third-order nonlinear ordinary differential equations

作　　者：邓正平 李永祥 DENG Zheng-Ping;LI Yong-Xiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《四川大学学报（自然科学版）》2019年第5期792-796,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11261053; 11661071)

摘　　要：本文讨论如下一般三阶常微分方程周期边值问题Lu(t)=f(t,u(t),u′(t),u″(t)),t∈[0,ω],u(k)(0)=u(k)(ω),k=0,1,2解的存在性,其中Lu(t)=u(t)+a 2u″(t)+a 1u′(t)+a 0u(t)是三阶常微分算子,f:[0,w]×R 3→R连续.在非线性项f满足适当的增长条件下,本文应用Fourier分析法与Leray-Schauder不动点定理获得了该问题解的存在唯一性.In this paper,the existence of solutions for the following third-order ordinary differential equation periodic boundary value problem Lu(t)=f(t,u(t),u′(t),u″(t)),t∈[0,ω],u(k)(0)=u(k)(ω),k=0,1,2 is considered,where Lu(t)=u(t)+a 2u″(t)+a 1u′(t)+a 0u(t)is third-order ordinary differential operator,f:[0,w]×R 3→R is continuous.Applying the Fourier analysis method and Leray-Schauder fixed point theorem,we obtain the existence and uniqueness of the solutions of the equation when the nonlinear term f satisfies some proper growth conditions.

关 键 词：三阶周期边值问题 FOURIER级数 LERAY-SCHAUDER不动点定理 

分 类 号：O175.15[理学—数学]