The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems

Zhou Qin-de; Li Yong

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Zhou Qin-de, Li Yong. The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems[J]. Applied Mathematics and Mechanics, 1989, 10(6): 553-557.

Citation:

Zhou Qin-de, Li Yong. The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems[J]. Applied Mathematics and Mechanics, 1989, 10(6): 553-557.

Citation:

Zhou Qin-de, Li Yong. The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems[J]. Applied Mathematics and Mechanics, 1989, 10(6): 553-557.

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The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems

Dept. of Math., Jilin Univ., Changchun

Received Date: 1986-09-17
Publish Date: 1989-06-15

Abstract

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: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.

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References(7)

References

[1]	Fife,P.C.,Semilinear elliptic boundary value problems with small parameters,Arch.Ration Mach.Anal.,52,3(1973),205-232.
[2]	Howes,F.A.,A class of boundary value problems whose solutions possess angular limiting behavior,Rocky Min.J Math.,6(1976),591-607.
[3]	Howes,F.A.,Singularly perturbed semilinear systems,Stud Appl.Math.,61(1979),185-209.
[4]	O'Donnell,M.A.,Boundary and corner layer behavior in singularly perturbed semilinear systems boundary value problems,SIAM J.Math.Anal.,2(1984),317-332.
[5]	章国华、刘光旭,奇摄动半线性系统的边界层和角层性质,应用数学和力学,5,3 (1984),337-344.
[6]	林宗池、倪守平,算子与边界双摄动的非线性方程边值问题的奇摄动,数学杂志,3,3 (1983),205-216.
[7]	Nagumo,M.,Über die differentialgleichung y"=f(x,y,y'),Proc.Phys.Math.Soc.Japan,19(1937),861-866.