奇异摄动边值问题的渐近展开

本文研究了奇异摄动边值问题:εy"=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε),其中ε是一个正小参数.在条件f_y(0,y,0)≥m₀(>0),f_y(1,y,0)≥m₀和f_y(t,y,ε)≥0之下.我们证明了解的存在唯一性,并给出了解的一致有效渐近展开式,从而改进了已有的结果.

The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems

In this paper we study the singularly penurbed boundary value problem:εy"=f(t,y,ε), y(0)=ξ(ε),y(1)=η(ε), where ε is a positive small parameter In the conditions:f_y(0,y,0)≥m₀,f_y(1,y,0)≥m₀ and f_y(t,y,ε)≥0, we prove the existences, and uniformly valid asymptotic expansions of solutions for the given boundary value problems, and hence we improve the existing results.