| 不动点定理在奇摄动非线性初值问题的套层解中的应用 |
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| 引用本文： | 程燕.不动点定理在奇摄动非线性初值问题的套层解中的应用[J].数学季刊,2003,18(1):103-107. |
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| 作者姓名： | 程燕 |
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| 作者单位： | Department of Basic Course，Artillery Academy of P.L.A.，Hefei 230031，China |
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| 摘 要： | Singularperturbationofnonlinearboundaryvalueproblemswhichhavedoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofdifferentialinequali ties1 ] -3 ] .Nonlinearboundaryvalueproblemswhichhavenotdoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofthefixed_pointtheorem4] -6 ] .Inthispa perwewillusethefixed_pointtheoremtodiscussthethirdorderdifferentialequationswhichhavedoubleinitiallayer.Weconsiderthefollowingproblem .ε4y =h(t,y,εy′,ε2 y″,ε) ,t∈ 0 ,T…
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| 关 键 词： | 应用 不动点理论 “Jacketed解” 奇异扰动非线性问题 常微分方程 边值问题 渐进展开 |
The Application of the Fixed-point Theory in Jacketed Solution of Singularly Perturbed Nonlinear Problem |
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| CHENG Yan.The Application of the Fixed-point Theory in Jacketed Solution of Singularly Perturbed Nonlinear Problem[J].Chinese Quarterly Journal of Mathematics,2003,18(1):103-107. |
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| Authors: | CHENG Yan |
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| Institution: | DepartmentofBasicCourse,ArtilleryAcademyofP.L.A.Hefei230031,China |
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| Abstract: | In this paper,the fixed-point theorem is used to estimated an asymptotic solution of intial val-ue problems for a class of third nonlinear differential equations which has double initial-layer properties.We obtain the uniformly valid asymptotic expansion of any orders including boundary layers. |
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| Keywords: | fixed_point theorem asymptotic expansion jacketed solution singular perturbation |
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