某些非线性三阶两点边值问题的正解存在性  

Existence of Positive Solutions for Some Nonlinear Third-Order Two-Point Boundary Value Problems

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《吉首大学学报（自然科学版）》2003年第2期10-14,共5页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(19801028)

摘　　要：考察了三阶非线性常微分方程的某些两点边值问题的正解存在性.这一类边值问题来源于粘性液体流动的研究,在流体力学中具有广泛的应用.已有学者在非线性项超线性或次线性的情况下获得了上述问题的正解存在性.通过改进其使用的方法,在非线性项既不是超线性,又不是次线性的条件下给出了关于这类问题正解的2个存在定理.方法是:(1)利用相应边值问题的Green函数将该问题转化为连续函数空间上的积分方程;(2)根据Green函数的性质选择适当的锥;(3)利用锥压缩与锥拉伸型的Krasnoselskii不动点定理获得了2个正解存在定理.结果表明已有的主要结论是本文结论的特殊情况.The existence of positive solution to some two-point boundary value problems are considered for third-order nonlinear ordinary differential equation.This class of boundary value problems arises from the investigation for flow of sticky liquid and possesses wide application in liquid mechanics.In recent years,Professor Jiang Daqing has obtained the existence of positive solution under the condition where nonlinear term is superlinear or sublinear.By improving the method used by Jiang,the author give two existence theorems of the class of problems under the condition where the nonlinear term is neither superlinear nor sublinear.The processes are as follows: (1) By applying the Green functions of corresponding boundary value problems the problems are transformed to integral equations on the space of continuous functions; (2) By applying the properties of Green functions the suitable cones are chosen; (3) By making use of Krasnoselskii fixed point theorem of cone expansion-compression type,two existence theorems of positive solution are obtained.This paper implies that Jiang's main conclusions are the special cases of our results.

关 键 词：三阶非线性常微分方程 三阶两点边值问题 正解 GREEN函数 连续函数 存在性 

分 类 号：O175.8[理学—数学] O175.14[理学—基础数学]