| 边界层函数法在微分不等式中的应用 |
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| 引用本文： | 倪明康,林武忠. 边界层函数法在微分不等式中的应用[J]. 华东师范大学学报(自然科学版), 2007, 2007(3): 1-10 |
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| 作者姓名： | 倪明康 林武忠 |
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| 作者单位： | 华东师范大学数学系,上海,200062;上海高校计算科学E-研究院,上海交通大学研究所,上海,200062 |
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| 基金项目： | 国家自然科学基金 , 上海市教委资助项目 , 江苏省重点建设实验室基金 , 上海市浦江人才计划 |
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| 摘 要： | 针对一类常微分方程奇摄动边值问题, 介绍了用Vasil’eva,边界层函数法来构造Nagumo定理中的上下解, 并用微分不等式证明了解的存在性和进行了余项估计. 用边界层函数法来构造上下解更具有普遍性, 且使用方便.
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| 关 键 词： | 奇摄动 渐近解 上下解 奇摄动 渐近解 上下解 |
| 文章编号： | 1000-5641（2007）03-0001-10 |
| 收稿时间： | 2007-01-01 |
| 修稿时间： | 2007-01-01 |
Application of Boundary Layer Function Method in Differential Inequality(Chinese) |
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| NI Ming-kang,LIN Wu-zhong. Application of Boundary Layer Function Method in Differential Inequality(Chinese)[J]. Journal of East China Normal University(Natural Science), 2007, 2007(3): 1-10 |
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| Authors: | NI Ming-kang LIN Wu-zhong |
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| Affiliation: | 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China |
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| Abstract: | This paper discussed a kind of singularly perturbed ODE with boundary value. The upper and lower solutions defined in Nagumo Theorem by means of Vasil'eva's boundary layer function method were contructed. Actually, it is of great universality and easy to use. After the construction, the existence of the solution of this singularly perturbed problem and estimation of the remainder terms with differential estimation of inequalities was proved. |
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| Keywords: | singular perturbation asymptotic solution upper and lower solutions |
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