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拟线性常微分方程组边值问题解的估计
引用本文:黄蔚章.拟线性常微分方程组边值问题解的估计[J].应用数学和力学,1992,13(8):719-727.
作者姓名:黄蔚章
作者单位:福建师大福清分校
摘    要:本文研究拟线性常微分方程组边值问题x′=f(t,x,y,ε),x(0,ε)=A(ε)εy″=g(t,x,y,ε)y′+h(t,x,y,ε)y(0,ε)=B(ε),y(1,ε)=C(ε)的奇摄动。其中x,f,y,h,A,B和C均属于R~n,g是n×n矩阵函数。在适当的条件下,利用对角化技巧和不动点定理证明解的存在,并估计了余项.

关 键 词:拟线性  常微分方程组  边值问题

The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations
Huang Wei-zhang.The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations[J].Applied Mathematics and Mechanics,1992,13(8):719-727.
Authors:Huang Wei-zhang
Abstract:This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations where x, f, yt h. A, B, and C all belong to Rn,and g is an nxn matrix function. Under suitable conditions we prove the existence of the solutions by diago-nalization and the fixed point theorem and also estimate the remainder.
Keywords:systems of the quasi-linear ordinary differential equation  singular perturbation  diagonalization  asymptotic expansion
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