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.
In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales. The paradox in[1] and the variational approach in [2] are avoided. The uniformly valid asymptotic approximations of solutions have been constructed. We also study the case which does not exhibit resonance.
出处
《应用数学和力学》
CSCD
北大核心
1991年第2期109-117,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金
关键词
常微分方程
奇异摄动
转点问题
ordinary differential equation
singular perturbation
turning point problem
