缺乏单调性的奇异三阶三点边值问题的正解(英文)  

Positive Solutions of Singular Third-order Three-point Boundary Value Problems without Monotonicity

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：《应用数学》2010年第2期353-357,共5页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation (10571085)

摘　　要：考虑了非线性三阶三点边值问题u′′′(t)=f(t,u(t))+g(t,u(t)),0<t<1,u(0)=u′(η)=u′′(1)=0的正解.本文中g(t,u)可以在t=0,t=1及u=0处奇异,而且允许g(t,u)关于u不是非减的.通过构造适当的控制函数并且利用锥上的Guo-Krasnoselskii不动点定理,证明了若干新的局部存在定理.The positive solutions of the nonlinear third-order three-point boundary value problem u＇＇＇（t）=f（t,u（t））＋g（t,u（t））,0t1,u（0）=u＇（η）=u＇＇（1）=0 are considered.In this paper,g（t,u） may be singular at t=0,t=1 and u=0.Moreover,g（t,u） is allowed to be not nondecreasing in u.By constructing suitable control functions and using the Guo-Krasnosel＇skii fixed point theorem on cone,several new local existence theorems are proved.

关 键 词：常微分方程 多点边值问题 奇异非线性 正解 

分 类 号：O175.8[理学—数学]