临界情况一般非线性边值问题

A Critical Case of the General Nonlinear Boundary Value Problem

对微分方程μ(dn)/(dt)=F(x,t,μ)及边值条件R(x(0,μ),x(1,μ))=0,其中x,F,R皆为M维向量,本文运用??边界层函数法,借助于临界情况的初值问题,进一步对具有单边界层的临界情况边值问题进行专门讨论.给出了解存在唯一的充分条件.

The differential equations μ(dx)/(dt)=F(x,t, μ,) with boundary condition R(x(0, μ), x(1, μ))=0 are discussed where x, F, Rare m-dimensipn vectors.The method of Vasilevas' boundary layer function and the results on critial case of initial value problems are used to study the critical case of boundary value problem with a single boundary layer.Sufficient conditions for the existence and uniqueness of solutions are given.