具有Caratheodory函数的四阶边值问题(英文)  

Fourth order boundary value problem with Caratheodory function

作　　者：孔令彬[1] 蒋达清[2] 

机构地区：[1]大庆石油学院数学系,安达151400 [2]东北师范大学数学系,长春130024

出　　处：《纯粹数学与应用数学》2000年第2期61-68,共8页Pure and Applied Mathematics

摘　　要：利用上下解方法和Schauder不动点定理 ,讨论了一类具有Caratheodory函数的四阶边值问题 。Fourth order boundary value problemu (4) (t)=f(t,u(t),u″(t)) for a.e.t∈I=[a,b], u (i) (a)-u (i) (b)=λ i∈R,i=0,1,2,3.is studied in this paper by using the generalized method of lower and upper solutions and Schauder fixed point theorem,where f is a Carathéodory function.Under suitable conditions on f,it is proved that the problem has a solution if and only if there exist a lower solution α(t) and an upper solution β(t) with α″(t)+mα(t)≤β″(t)+mβ(t) on [a,b],m∈(-∞,0)∪(0,(πb-a) 2].

关 键 词：四阶边值问题 上下解 CARATHEODORY函数 

分 类 号：O175.8[理学—数学]