| 非线性变系数二阶Neumann边值问题的正解 |
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| 引用本文： | 姚庆六.非线性变系数二阶Neumann边值问题的正解[J].山东大学学报(理学版),2007,42(12):10-14. |
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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,江苏,南京,210003 |
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| 摘 要： | Neumann边值问题描述了在边界点处梯度为零的大量物理现象。 本文利用锥上的不动点指数定理研究了带有函数系数k(t)的非线性二阶Neumann边值问题u″(t)+k(t)u(t)=f(t,u(t)),0≤t≤1,u′(0)=u′(1)=0的正解。 主要结论表明,只要非线性项在某些有界集合上的增长速度 是适当的, 该问题就具有n个正解, 其中n是一个任意的自然数。
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| 关 键 词： | 非线性常微分方程 Neumann边值问题 正解 存在性 多解性 |
| 文章编号： | 1671-9352（2007）12-0010-05 |
| 收稿时间： | 2007-07-23 |
| 修稿时间： | 2007年7月23日 |
Positive solutions of nonlinear second-order Neumann boundary value problems with a variable coefficient |
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| YAO Qing-liu.Positive solutions of nonlinear second-order Neumann boundary value problems with a variable coefficient[J].Journal of Shandong University,2007,42(12):10-14. |
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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, Jiangsu, China |
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| Abstract: | Neumann boundary value problems describe many physical phenomena whose gradients are zero at boundary points. The positive solutions of nonlinear second-order Neumann boundary value problem u″(t)+k(t)u(t)=f(t,u(t)), 0≤t≤1, u′(0)=u′(1)=0 with function coefficient k(t)were studied by applying the fixed-point index theorem of cones. The main results show that the problem has n positive solutions provided growth rates of nonlinear term on some bounded sets are appropriate, where n is an arbitrary natural number. |
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| Keywords: | nonlinear ordinary differential equation Neumann boundary value problem positive solution existence multiplicity |
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