On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points

Jiang Fu-ru

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Jiang Fu-ru. On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1980, 1(2): 201-213.

Citation:

Jiang Fu-ru. On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1980, 1(2): 201-213.

Citation:

Jiang Fu-ru. On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1980, 1(2): 201-213.

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On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points

Jiang Fu-ru

Fudan University, Shanghai

Received Date: 1979-12-28
Publish Date: 1980-04-15

Abstract

Abstract

In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales.The paradox in[1] and the variational approach in [2] are avoided,The uniformly valid asymptotic approximations of solutions have been constructed.We also study the case which does not exhibit resonance.

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References(5)

References

[1]	Ackerberg,R.C.and O'Malley,R.E.Jr Boundary layer problem exhibiting resonance,Studies in Appl.Math.,49,3,(1970),277-295.
[2]	Grasman,J.,and Matkowsky,B.J.,A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points,SI AM I.Appl.Math.,32,3,(1977),588-597.
[3]	Nayfeh,A.H,,Perturbation Methods,Wiley,New York,(1973).
[4]	Cook,L.P and Eckhaus,W,,Resonance in a boundary value problem of singular perturbation type,Studies in A ppl.Math,,52.,2,(1973),129-139.
[5]	Matkowsky,B.J.,On boundary layer problem exhibiting resonance,SIAM Rev,17.1.(1975).82-100.