拟线性常微分方程组边值问题解的估计
The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations
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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Rn,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.Abstract: This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations 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) where x,f, y, h, A, B and C all belong to Rn, and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.
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