非线性边值问题的奇摄动

章国华; 林宗池

非线性边值问题的奇摄动

章国华¹,
林宗池²

1.
卡技利大学加拿大;
2.
福建师范大学

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出版历程
- 收稿日期: 1984-02-05
- 刊出日期: 1984-10-15

Singular Perturbation of Nonlinear Boundary Value Problem

K. W. Chang¹,
Lin Zong-chi²

1.
University of Calgary, Canada;
2.
Fujian Normal University, Fuzhou

摘要

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f_y’≤-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y_i-j,j(x)(j=0,1,…,i;i=1,2,…m)能够从某些线性方程逐次求得.

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 ƒy'≤-k<0 and other suitable restrictions,there exists a solution and it satisfied where yo,o(x) is solution of reduced problem ƒ(x,y,y')=0(01(0,0) while y_1-j,j(x)(j=0,1…,i;i=1,2…,m)'can be obtained successively from certain linear equations.

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参考文献(12)

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