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.
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.
出处
《应用数学和力学》
EI
CSCD
北大核心
1992年第8期719-727,共9页
Applied Mathematics and Mechanics
关键词
拟线性
常微分方程组
边值问题
systems of the quasi-linear ordinary differential equation, singular perturbation, diagonalization, asymptotic expansion
