关于具有转点的常微分方程的边值问题*
On the Boundary Value Problems for Ordinary Differential Equations with Turning Points
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摘要: 本文研究下面形式的边值问题εy"-f(x,ε)y'+g(x,ε)y=0(-α≤x≤b,0<ε≤1)y(-α)=α,y(b)=β其中f(x,0)在区间[-a,b]上具有多个和多重零点.给出了出现边界层和内部层的条件,并在相应的条件下,构造解的渐近展开式.Abstract: In this paper, we consider the boundary value problems of the form ey"-f(x,e)y'+g(x,e)y=0(-a≤x≤b,0<ε≤1)y(-a)=a,y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.
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