| 三阶非线性微分方程边值问题的奇摄动 |
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| 引用本文： | 陈松林.三阶非线性微分方程边值问题的奇摄动[J].安徽工业大学学报,1992(1). |
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| 作者姓名： | 陈松林 |
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| 作者单位： | 华东冶金学院基础课部 |
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| 摘 要： | 本文先提出一类三阶非线性微分方程的两点边值问题,利用Nagumo条件和上下解的技巧,讨论上述问题解的存在性和解的估计;然后,运用该结果,研究相应的奇摄动问题。在适当的条件下,得到该问题的在整个区间上达到任意精度的一致有效的渐近解
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| 关 键 词： | 奇摄动 边值问题 非线性微分方程 上下解 |
Singular Perturbation for a Boundary Value Problem of Third Order Nonlinear Differential Equation |
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| Chen Songling.Singular Perturbation for a Boundary Value Problem of Third Order Nonlinear Differential Equation[J].Journal of Anhui University of Technology,1992(1). |
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| Authors: | Chen Songling |
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| Affiliation: | Common Course Department |
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| Abstract: | In this paper, a boundary value problem of third order nonlinear differential equation is presented and the existence of its solutions is discussed by using lower and upper solutions and a Nagumo condition. Then the results obtained above are applied to the corresponding singularly perturbed problem. Finally, under some suitable conditions, the uniformly valid asymptotic expansion to any degree of precision is given to the solution of the singularly perturbed proglem on the entire interval. |
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| Keywords: | Singular perturbation Boundary value problem Nonlinear differential equation Upper and lower solutions |
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