| 半正Neumann边值问题的解和正解的存在性与多解性 |
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| 引用本文： | 姚庆六,李永祥.半正Neumann边值问题的解和正解的存在性与多解性[J].西南交通大学学报,2005,40(4):539-543. |
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| 作者姓名： | 姚庆六 李永祥 |
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| 作者单位： | 1. 南京财经大学应用数学系,江苏,南京,210003
2. 西北师范大学数学与信息科学学院,甘肃,兰州,730070 |
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| 基金项目： | 甘肃省自然科学基金资助项目（ZS031-A25-003-Z） |
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| 摘 要： | 利用锥拉伸与锥压缩型的Krasnosel＇skii不动点定理考察了一类非线性Neumann边值问题的解和正解，其中允许非线性项有非正的下界．研究表明，只要非线性项在某些有界集上的最大高度和最小高度是适当的，这个问题便具有n（n为任意自然数）个解或者正解．
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| 关 键 词： | 存在性 多解性 二阶常微分方程 Neumann边值问题 解和正解 |
| 文章编号： | 0258-2724（2005）04-0539-05 |
| 收稿时间： | 2005-01-10 |
| 修稿时间： | 2005-01-10 |
Existence and Multiplicity of Solutions and Positive Solutions for Semipositive Neumann Boundary Value Problems |
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| YAO Qing-liu,LI Yong-xiang.Existence and Multiplicity of Solutions and Positive Solutions for Semipositive Neumann Boundary Value Problems[J].Journal of Southwest Jiaotong University,2005,40(4):539-543. |
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| Authors: | YAO Qing-liu LI Yong-xiang |
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| Institution: | 1. Dept. of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China; 2. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | By using cone expansion-compression fixed point theorem, the solutions and positive solutions were studied for the nonlinear Neumarm boundary value problem, where the nonlinear term was allowed to have a nonpositive lower bound. It is shown that the problem has n solutions or positive solutions provided the maximum and minimum heights of the nonlinear terms are appropriate on some bounded sets, where n is a natural number. |
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| Keywords: | existence multiplicity of solutions second order differential equation Neumann boundary value problem positive solution |
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