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Applied Mathematics and Mechanics

, Volume 9, Issue 9, pp 873–880 | Cite as

Singular perturbation of nonlinear vector boundary value problem

  • Kang Sheng-liang
  • Chen Qi
Article

Abstract

In this paper we study the perturbed boundary value problem of the form
$$\begin{gathered} dx/dt = f(x,y,t;\varepsilon ),\varepsilon dy/dt = g(x,y,t;\varepsilon ), \hfill \\ a_1 (\varepsilon )x(0,\varepsilon ) + a_2 (\varepsilon )y(0,\varepsilon ) = a(\varepsilon ) \hfill \\ b_1 (\varepsilon )x(1,\varepsilon ) + \varepsilon b_2 (\varepsilon )y(1,\varepsilon ) = \beta (\varepsilon ) \hfill \\ \end{gathered}$$
in which x, f, β∈Em, y, g, a∈En, 0<ε≪1 and a1(ε), a2(ε), b1(ε) and b2(ε) are matrices of the appropriate size. Under the condition that gγ(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.

Keywords

Manifold Unique Solution Asymptotic Expansion Chert Singular Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    O'Malley, R.E., Singular perturbation of a boundary value problem for a system of nonlinear differential equations,J. Differential Equations, 8 (1970), 431–447.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Jiang Fu-ru, On singular perturbation of nonlinear boundary value problems for ordinary differential equations,Scientia Sinica (A), 3 (1985), 232–242.Google Scholar
  3. [3]
    Hoppensteadt, F., Properties of solutions of ordinary differential equations with small parameters,Comm. Pure. Appl. Math.,26 (1971), 807–840.MathSciNetGoogle Scholar
  4. [4]
    Chang, K.W. and W.A. Coppel, Singular perturbations of initial value problem over a finite interval,Arch. Rat. Mech. Anal. 32 (1969), 268–280.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© SUT 1988

Authors and Affiliations

  • Kang Sheng-liang
    • 1
  • Chen Qi
    • 1
  1. 1.Tongji UniversityShanghai

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