奇摄动非线性系统边值问题*

本文利用对角化技巧和方法讨论二阶奇摄动非线性系统边值问题εy"＝f(t,y,y',ε),y(0,ε)＝α(ε),y(1,ε)＝b(ε)当Jacobi矩阵fy'的特征值有K个负实部和N－K个正实部时,解的存在性及其渐近性质。

Boundary Value Problem for a Singularly Perturbed Nonlinear System

In this paper, by the technique and the method of deagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with:εy"=f(t,y,y',ε),y(0,ε)=a(ε),y(1,ε)=b(ε) The existance of the solution and its asymptotic properties are discussed when the eigenvaslues of Jacobi matrix fy' has K negative real parts and N-K positve real parts.