奇异摄动边值问题的渐近展开
The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems
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摘要: 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fy(0,y,0)≥m0(>0),fy(1,y,0)≥m0和fy(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.Abstract: 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:fy(0,y,0)≥m0,fy(1,y,0)≥m0 and fy(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.
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