三阶周期边值问题的正解问题  

Positive solution of third order periodic boundary value problem

作　　者：胡金燕[1] 杨云峰[1] 

机构地区：[1]大庆石油学院数学科学与技术学院,黑龙江大庆163318

出　　处：《大庆石油学院学报》2007年第2期99-101,共3页Journal of Daqing Petroleum Institute

摘　　要：利用上下解方法和Schauder不动点定理,证明三阶周期边值问题u+ρ3u=f(t,u),0≤t≤2π,u(i)(0)=u(i)(0)=u(i)(2π),i=0,1,2,存在正解的充要条件是存在下解α(t)和上解β(t),并满足β′+ρβ≤α′+ρα,ρ∈(0,1/3),f是一个非负的Caratheodory函数.Third order periodic boundary value problem, u+ρ3u=f(t,u),0≤t≤2π,u(i)(0)=u(i)(2π),i=0,1,2, is studied by using the method of lower and upper solutions and Schauder fixed point theorem when f is a Caratheodory function. It is proved that the problem has a solution if and only if there exists a lower solution α(t) and an upper solution β(t) with β′+ρβ≤α′+ρα, where ρ∈(0,1/3).

关 键 词：三阶周期边值问题 上下解 SCHAUDER不动点定理 正解 

分 类 号：O175[理学—数学]