拟线性常微分方程组边值问题解的估计

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The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations

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.
- 拟线性常微分方程组 /
- 奇异摄动 /
- 对角化 /
- 渐近展开
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.
- systems of the quasi-linear ordinary differential equation /
- singular perturbation /
- diagonalization /
- asymptotic expansion

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