含一阶导数项的三阶周期边值问题解的存在唯一性  

Existence and Uniqueness Result for Third-order Periodic Boundary Value Problem with the First Derivatives

作　　者：白婧[1] 李永祥[1] 

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：《四川师范大学学报（自然科学版）》2015年第6期834-837,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11261053);甘肃省自然科学基金(1208R-JZA129)

摘　　要：三阶常微分方程的周期边值问题一直是常微分方程研究的热点.研究非线性项含一阶导数项的三阶周期边值问题{u^m(t)=f(t,u(t),u'(t)),t∈[0,ω],u^((i))(0)=u^((i))(ω),i=0,1,2,其中,f:[0,ω]×R^2→R连续,通过Fourier分析的方法及非线性项的扰动技巧,利用Leray-Schauder不动点定理得出解的存在性与唯一性.之前的许多研究主要集中在非线性项不含导数项的情形,对之前所得结论进行了推广.Third-order periodic boundary value problem has always been the hot of the ordinary differential equation. In this paper, we discuss the solvability of the third-order periodic boundary value problem with nonlinear term {u^m（t）=f（t,u（t）,u＇（t））,t∈[0,ω],u^（（i））（0）=u^（（i））（ω）,i=0,1,2, where f：[0,ω]×R^2→R is a continuous function. Using the method of Fourier analysis and the perturbation technique of nonlinear term, the existence and uniqueness of solution are obtained by Leray-Sehauder fixed point theorem. Since many former studies have focused on nonlinear term without derivative, our results generalize the previous conclusions.

关 键 词：三阶周期边值问题 存在性与唯一性 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]