| 一类二阶非线性边值问题的正解 |
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| 引用本文： | 翟成波.一类二阶非线性边值问题的正解[J].数学的实践与认识,2005,35(4):233-237. |
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| 作者姓名： | 翟成波 |
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| 作者单位： | 山西大学数学系,山西,太原,030006 |
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| 基金项目： | 国家自然科学基金 (1 0 3 71 0 68)，山西省自然科学基金 (2 0 0 41 0 0 3 ) |
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| 摘 要： | 利用Kransnosel′skii锥拉伸锥压缩不动点定理及不动点指数理论,讨论了一类二阶非线性边值问题u″+a(t) f (u) =0 ,t∈(0 ,1 ) ,αu(0 ) -βu′(0 ) =0 ,γu(1 ) +δu′(1 ) =0 正解的存在性与多重性.函数a允许在端点t=0和t=1具有奇性.
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| 关 键 词： | 二阶边值问题 正解 锥 不动点 |
| 修稿时间： | 2005年1月14日 |
Positive Solutions for a Class of Second-Order Nonlinear Boundary Value Problem |
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| ZHAI Cheng-bo.Positive Solutions for a Class of Second-Order Nonlinear Boundary Value Problem[J].Mathematics in Practice and Theory,2005,35(4):233-237. |
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| Authors: | ZHAI Cheng-bo |
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| Abstract: | The existence and multiplicity of positive solutions for second-order nonlinear boundary value problems u″+a(t)f(u)=0, t∈(0,1), αu(0)-βu′(0)=0, γu(1)+δu′(1)=0 are studied by using the Kransnosel′skii fixed-point theorem of cone expansion-compression type and the fixed-point index results, where a is allowed to be singular at both end points t=0 and t=1. |
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| Keywords: | second-order BVP positive solution cone fixed-point |
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