| 一类非线性奇摄动问题的渐近解 |
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| 引用本文： | 陈埰旺,唐荣荣. 一类非线性奇摄动问题的渐近解[J]. 丽水学院学报, 2009, 31(5): 13-16. DOI: 10.3969/j.issm.1008-6749.2009.05.005 |
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| 作者姓名： | 陈埰旺 唐荣荣 |
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| 作者单位： | 湖州师范学院理学院,浙江湖州,313000 |
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| 摘 要： | 利用奇异摄动的相关理论，研究了一类非线性奇摄动边值问题。首先求得原问题的内部解和外部解。其次，在适当的条件下，使用匹配原则y=Y°，匹配原问题的内、外部解，解得待定常数，继而得到参数k取不同值时该问题解的渐近展开式。从而推广了文献（王莉婕．一类非线性奇摄动问题的匹配解法．大学数学，2005，21（4）：46—48）中的相应结论，并且也为估计相关类型非线性问题的解提供了一种有效的方法。
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| 关 键 词： | 非线性 奇摄动 匹配 渐近展开式 |
The Asymptotic Solution for a Class of Nonlinear Singularly Perturbed Problems |
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| Chen Caiwang,Tang Rongrong. The Asymptotic Solution for a Class of Nonlinear Singularly Perturbed Problems[J]. Journal of Lishui University, 2009, 31(5): 13-16. DOI: 10.3969/j.issm.1008-6749.2009.05.005 |
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| Authors: | Chen Caiwang Tang Rongrong |
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| Affiliation: | ( College of Science, Huzhou Teachers College, Huzhou Zhejiang 313000, China ) |
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| Abstract: | U sing the theory of singularly perturbations,the author studied a class ot nonlinear slngutany perturbed boundary value problems. Firstly the author, obtained the internal and outer solutions of the original problem. Secondly,under the appropriate conditions,he got the asymptotic expansions of solution for the problem by matching the internal and outer solutions of original problem, when the parameters F in different values, which popularized the correspondent results in paper, and provides an effective method for estimating the solution related to some class of nonlinear problems. |
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| Keywords: | nonlinear singularly perturbation matching asymptotic expansion |
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