具有Caratheodory函数的四阶边值问题(英文) 被引量：1

Fourth order boundary value problem with Caratheodory function

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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].

作者孔令彬蒋达清

机构地区大庆石油学院数学系东北师范大学数学系

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

关键词四阶边值问题上下解 CARATHEODORY函数 fourth order boundary value problem lower and upper solutions Schauder fixed point theorem

分类号 O175.8 [理学—基础数学]

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