一类复合型奇异三阶三点边值问题正解的存在性  

Existence theorems of positive solution to a class of third-order three-point boundary value problems of composite type

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,江苏南京210003

出　　处：《浙江大学学报（理学版）》2012年第4期381-384,共4页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11071109)

摘　　要：考察了一类复合型非线性三阶三点边值问题的正解,其中非线性项f(t,u)可以在t=0,t=1及u=0处奇异.利用锥压缩与锥拉伸型的Krasnosel'skii不动点定理建立了几个正解存在定理.当f(t,u)超线性和次线性时,这些存在定理推广了现有的结论.The positive solution is considered for a class of nonlinear third-order three-point boundary value problems of composite type,where the nonlinear term f(t,u)may be singular at t=0,t=1and u=0.By applying the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type,some existence theorems of positive solutions are established.The existing result is extended by these existence theorems when f(t,u)is superlinear and sublinear.

关 键 词：奇异常微分方程 多点边值问题 正解 存在性 多解性 

分 类 号：O17[理学—数学]