非线性边值问题的奇摄动 |
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引用本文: | 章国华,林宗池. 非线性边值问题的奇摄动[J]. 应用数学和力学, 1984, 5(5): 603-612 |
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作者姓名: | 章国华 林宗池 |
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作者单位: | 1.卡技利大学 加拿大; |
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摘 要: | 本文研究边值问题:εy"=f(x,y,y',ε,μ)(μ0(ε,μ)y(x,ε,μ)|(x=1-μ)=φ1(ε,μ)其中ε,μ是两个正的小参数 在fy’≤-k<0和其他适当的限制下,存在一个解且满足其中y0,0(x)是退化问题 f(x,y,y',0,0)=0(01(0,0)的解,而yi-j,j(x)(j=0,1,…,i;i=1,2,…m)能够从某些线性方程逐次求得.
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收稿时间: | 1984-02-05 |
Singular Perturbation of Nonlinear Boundary Value Problem |
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Affiliation: | 1.University of Calgary, Canada;2.Fujian Normal University, Fuzhou |
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Abstract: | In this paper we consider the boundary value problemwhere εy"=f(x,y,y',ε,μ)(μ0(ε,μ)y(x,ε,μ)|(x=1-μ)=φ1(ε,μ) where ε,μ,are two positive parameters. Under ?y'≤-k<0 and other suitable restrictions,there exists a solution and it satisfied where yo,o(x) is solution of reduced problem ?(x,y,y')=0(01(0,0) while y1-j,j(x)(j=0,1…,i;i=1,2…,m)'can be obtained successively from certain linear equations. |
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