三阶周期边值问题的正解存在性  

Positive Solution of Third Order Periodic Boundary Value Problem

作　　者：孔令彬[1] 王玉学[1] 

机构地区：[1]大庆石油学院数学系,黑龙江安达151400

出　　处：《哈尔滨理工大学学报》2000年第6期10-12,共3页Journal of Harbin University of Science and Technology

摘　　要：利用上下解方法和Ｓｃｈａｕｄｅｒ不动点定理，证明了三阶周期边值问题ｕ＂＇＝ｆ（ｔ，ｕ），０≤ｔ≤２π；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）并且满足α’＋ｍα≥β＇＋ｍβ， ｍ∈（０，１］，ｆ是一个非负的Ｃａｒａｔｈｅｄｏｒｙ函数．Third order periodic boundary value problem u'' = f (t, u), 0 ≤ t≤2π, with 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, where 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' +mgβ≤ a' + ma, where m ∈ (0, ].

关 键 词：三阶周期边值问题 上下解 SCHAUDER不动点定理 CARATHEODORY函数 

分 类 号：O175[理学—数学]