On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters

Zhang Han-lin

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Article Navigation > Applied Mathematics and Mechanics > 1989 > 10(5): 453-461

Zhang Han-lin. On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters[J]. Applied Mathematics and Mechanics, 1989, 10(5): 453-461.

Citation:

Zhang Han-lin. On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters[J]. Applied Mathematics and Mechanics, 1989, 10(5): 453-461.

Citation:

Zhang Han-lin. On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters[J]. Applied Mathematics and Mechanics, 1989, 10(5): 453-461.

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On the Singular Perturbation of a Nonlinear Ordinary Differential Equation with Two Parameters

Zhang Han-lin

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

Received Date: 1988-02-29
Publish Date: 1989-05-15

Abstract

Abstract

In this paper,the method of differential inequalities has been applied to study the boundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

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References(13)

References

[1]	Chang,K.W.and F.A.Howes,Nonlinear perturbation phenomena:Theory and application,Appl.Math.Sci.,Springer-Verlag,New York Inc,56(1984).
[2]	O'Donnell,Mark,A.,Boundary and Corder layer behavior in singularly perturbed semilinear systems of boundary value problems,SIAM.J.Math.Anal.,15(1984),317-332.
[3]	Howes,F.A.,Differential inequalities and applications to nonlinear singular perturbationproblems,J.Diff.Equ.,20(1976),133-149.
[4]	Chang,K.W.,Diagonalization method for a vector boundary problem of singular perturbation type,J.Math.Anal.Appl.,48(1974),652-665.
[5]	Howes,F.A.,Effective characterization of the asymptotic behavior of solution of singularly perturbed boundary value problem,SIAM J.Appl.Math.,30,2(1976).
[6]	Howes,F.A.,Singularly perturbed semilinear Robin problem,Studies in Appl.Math.,67(1982) 125-139.
[7]	Mo Jia-qi,The estimation of singularly perturbed solution for a second order quasilinear equation via differential inequalities,J.Math.Res.and Exposition,1(1986),58-64.
[8]	O'Malley,R.E.Jr.,Singular perturbation of boundary value problem for linear ordinary differential equations involving two parameters,J.Math.Anal.Appl.,19(1967),291-308.
[9]	O'Malley,R.E.Jr.,Boundary value problems for linear systems of ordinary differential equations involving many parameters,J.Math.Mech.,18(1969),835-856.
[10]	O'Malley,R.E.Jr.On initial value problems for nonlinear systems of differential equations with two small parameters,Arch.Ration Mech.Anal.,40(1971),209-222.
[11]	Nagumo,M.,Über die Differential gleichung y"=f(x,y,y)Proc.Phys.Soc.Japan,19(1937),861-866.
[12]	Jackson,L.K.,Subfunctions and second-order ordinary differential inequalities,Advances in Math.,2(1968),307-363.
[13]	Heidel,J.W.,A Second-order nonlinear boundary value problem,J.Math.Anal,and Appl.,48(1974),493-503.