| 超线性条件下奇异二阶常微分方程三点边值问题正解的存在性 |
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| 引用本文： | 沈文国,宋兰安.超线性条件下奇异二阶常微分方程三点边值问题正解的存在性[J].山东大学学报(理学版),2007,42(6):91-94. |
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| 作者姓名： | 沈文国 宋兰安 |
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| 作者单位： | 1. 兰州工业高等专科学校基础学科部,甘肃,兰州,730050
2. 兰州工业高等专科学校,图书馆,甘肃,兰州,730050 |
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| 摘 要： | 应用锥上不动点定理，给出了奇异二阶常微分方程三点边值问题
x″(t)+f(t,x(t))=0, t∈(0,1),
x(0)=0, x(1)=kx(η).
存在C［0,1］正解的充分必要条件.这里η∈(0,1)是一个常数，f∈C((0,1)×［0,∞),［0,∞)).
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| 关 键 词： | 超线性 奇异非线性三点边值问题 正解 锥上不动点定理 |
| 文章编号： | 1671-9352（2007）06-0091-04 |
| 收稿时间： | 2006-10-23 |
| 修稿时间： | 2006-10-23 |
Existence of positive solutions for singular super-linear three-point boundary value problems of second order ordinary differential equations |
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| SHEN Wen-guo,SONG Lan-an.Existence of positive solutions for singular super-linear three-point boundary value problems of second order ordinary differential equations[J].Journal of Shandong University,2007,42(6):91-94. |
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| Authors: | SHEN Wen-guo SONG Lan-an |
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| Institution: | 1. The Basic Course Department of Lanzhou Polytechnic College, Lanzhou 730050, Gansu, China; 2. The Library of Lanzhou Polytechnic College, Lanzhou 730050, Gansu, China |
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| Abstract: | By means of the fixed point theorem on cons, a necessary and sufficient condition for the existence of C［0,1］ positive solutions are given to singular boundary value problems of a class of second order three point super linear differential equations
x″(t)+f(t,x(t))=0, t∈(0,1),
x(0)=0, x(1)=kx(η).
Where η∈(0,1) is a constant, f∈C((0,1)×［0,∞),［0,∞)). |
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| Keywords: | supedinear singular three-point boundary value problem positive solution fixedpoint theorem on cons |
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