| 带变号系数的非线性二阶两点边值问题的正解 |
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| 引用本文： | 姚庆六.带变号系数的非线性二阶两点边值问题的正解[J].郑州大学学报(理学版),2007,39(1):6-11. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学应用数学系,南京,210003 |
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| 摘 要： | 研究了非线性两点边值问题u″(t) h(t)f(u(t))=0,0≤t≤1,u(0)=u(1)=0的一、二及三个正解的存在性,其中,f≥0并且允许h在0,1]上改变符号,主要工具是锥压缩与锥拉伸型的Kras-nosel’skii不动点定理.
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| 关 键 词： | 非线性常微分方程 边值问题 正解 存在性 多解性 |
| 文章编号： | 1671-6841（2007）01-0006-06 |
| 修稿时间： | 2006-07-07 |
Positive Solutions of a Nonlinear Second-order Two-point Boundary Value Problem with Coefficient That Changes Sign |
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| YAO Qing-liu.Positive Solutions of a Nonlinear Second-order Two-point Boundary Value Problem with Coefficient That Changes Sign[J].Journal of Zhengzhou University:Natural Science Edition,2007,39(1):6-11. |
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| Authors: | YAO Qing-liu |
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| Institution: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China |
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| Abstract: | The existence of one,two and three positive solutions to the nonlinear two-point boundary value problem u"(t)+h(t)f(u(t))=0, u(0)=u(1)=0 is studied,where f≥0 and coefficient h is allowed to change sign on 0,1].Main tool is Krasnosel'skii fixed point theorem of cone expansion-compression type. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem positive solution existence multiplicity |
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