On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)

JIANG Fu-ru

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JIANG Fu-ru. On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(3): 239-249.

Citation:

JIANG Fu-ru. On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(3): 239-249.

Citation:

JIANG Fu-ru. On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(3): 239-249.

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On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)

JIANG Fu-ru

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

Received Date: 2000-03-21
Rev Recd Date: 2000-09-23
Publish Date: 2001-03-15

Abstract

Abstract

A new method is applied to study the asymptotic behavior of solutions of boundnary value problems for a class of systems of nonlinear differential equations u"=v,εv"+f(x,u,u')v'-g(x,u,u')v=0(0<ε≤1).The asymptotic expansions of solutions are constructed,the remainders are estimated.The former works are improved and generalized.
- system of nonlinear differential equations,
- boundary value problem,
- asymptotic solution

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References(6)

References

[1]	Dorr F W,Parter S V.Singular perturbations of nonlinear boundary value problems with turning points[J].J Math Anal Appl,1970,29:273-293.
[2]	Dorr F W,Parter S V.Shampine L F.Applications of the maximum principle to singular perturbation problems[J].SIAM Rev,1973,15:43-88.
[3]	Howes F A,Shao S.Asymptotic analysis of model problems for a coupled systems[J].Nonlinear Anal,1989,13(9):1013-1024.
[4]	Harris W A,Shao S.Refined approximations of the solutions of a coupled system with turning points[J].J Differential Equations,1991,92:125-144.
[5]	JIANG Fu-ru.On the boundary layer method[J].Appl Math and Mech(English Edition),1981,2(5):505-518.
[6]	JIANG Fu-ru.On the singular perturbations of nonlinear boundary value problems for ordinary differential equations[J].Scientia Sinica,1987,30(6):588-600.