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一类非线性三阶三点边值问题的解和正解
引用本文:姚庆六.一类非线性三阶三点边值问题的解和正解[J].数学杂志,2007,27(6):704-708.
作者姓名:姚庆六
作者单位:南京财经大学应用数学系,江苏南京,210003
摘    要:考察了一类含有一阶和二阶导数的非线性三阶三点边值问题的解和正解.通过构造适当的Banach空间并且利用相应的积分方程建立了两个存在定理.主要结论表明,只要非线性项在其定义域的某个子集上的"高度"是适当的,该问题存在一个解或者正解.

关 键 词:三阶常微分方程  三点边值问题  解和正解  存在性
文章编号:0255-7797(2007)06-0704-05
修稿时间:2005-04-05

SOLUTIONS AND POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEMS
YAO Qing-liu.SOLUTIONS AND POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEMS[J].Journal of Mathematics,2007,27(6):704-708.
Authors:YAO Qing-liu
Institution:Dept. of Applied Math. , Nanjing University of Finance and Economics, Nanjing 210003, China
Abstract:The solution and positive solution are considered for a class of nonlinear third-order three-point boundary value problems with first and second derivatives.By constructing suitable Banach space and applying corresponding integral equation,two existence theorems are established.The main results show that the problem has one solution or positive solution provided the "height" of nonlinear term is appropriate on some bounded subset of its domain.
Keywords:third-order ordinary differential equation  three-point boundary value problem  solution and positive solution  existence
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