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The shock solution to a class of singularly perturbed time delay nonlinear boundary value problem

  • School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.05.002
  • Received Date: 20 October 2016
  • Accepted Date: 10 May 2017
  • Rev Recd Date: 10 May 2017
  • Publish Date: 31 May 2018
    Abstract

  • Abstract

    The shock solution to a class of singularly perturbed time delay nonlinear boundary value problem were considered. The solution was obtained by using the matching asymptotic expansion, and the uniform validity of the solution was proved by the theory of differential inequalities.

    Abstract

    The shock solution to a class of singularly perturbed time delay nonlinear boundary value problem were considered. The solution was obtained by using the matching asymptotic expansion, and the uniform validity of the solution was proved by the theory of differential inequalities.
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    • References(10)
  • [1]
    陈兰荪.数学生态学模型与研究方法[M].北京：科学出版社,1988.
    [2]
    鲁世平.具非线性边界条件的Volterra型泛函微分方程边值问题奇摄动[J].应用数学与力学,2003,24(12):1276-1284.
    LU Shiping. Singularly perturbed nonlinear boundary value problem for a kind of volterra type functional differential equation[J]. Applied Mathematics and Mechanics, 2003,24(12): 1276-1284.
    [3]
    任景莉,葛渭高.具非线性边界条件的半线性时滞微分方程边值问题的奇摄动[J].应用数学与力学,2003,24(12):1285-1290.
    REN Jingli, GE Weigao. Singularly perturbed boundary value problems for semi-linear retarded differential equations with nonlinear boundary conditions[J]. Applied Mathematics and Mechanics, 2003,24(12):1285-1290.
    [4]
    鲁世平.奇摄动非线性时滞微分方程边值问题[J].数学研究与评论,2003,23(2):304-308.
    LU Shiping. Singularly perturbed boundary value problems for nonlinear differential equations with delay[J]. Journal of Mathematical Research and Exposition, 2003, 23(2):304-308.
    [5]
    ZHANG J F, ZHANG P A. Global asymptotic stability for a diffusion Lotka-Volterra competition system with time delays[J].Bull Korean Math Soc,2012,49(6):1255-1262.
    [6]
    SKRYNNIKOV Y. Solving initial value problem by matching asymptotic expansions[J].SIAM J Appl Math,2012,72(1): 405-416.
    [7]
    MO J Q, LIN W T, DU Z J. Singularly perturbed solution for nonlinear higher order elliptic equations with two parameters[J].J Sys Sci & Math,2013,33(2): 217-221.
    [8]
    MO J Q. Singularly perturbed reaction diffusion problem for nonlinear boundary condition with two parameters[J].Chin Phys,2010,19: 010203.
    [9]
    郑祖庥.泛函微分方程理论[M].合肥:安徽教育出版社,1994.
    [10]
    O’MALLEY JR R E. Introduction to Singular Perturbation[M]. New York: Academic Press, 1974.)
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    [1]
    陈兰荪.数学生态学模型与研究方法[M].北京：科学出版社,1988.
    [2]
    鲁世平.具非线性边界条件的Volterra型泛函微分方程边值问题奇摄动[J].应用数学与力学,2003,24(12):1276-1284.
    LU Shiping. Singularly perturbed nonlinear boundary value problem for a kind of volterra type functional differential equation[J]. Applied Mathematics and Mechanics, 2003,24(12): 1276-1284.
    [3]
    任景莉,葛渭高.具非线性边界条件的半线性时滞微分方程边值问题的奇摄动[J].应用数学与力学,2003,24(12):1285-1290.
    REN Jingli, GE Weigao. Singularly perturbed boundary value problems for semi-linear retarded differential equations with nonlinear boundary conditions[J]. Applied Mathematics and Mechanics, 2003,24(12):1285-1290.
    [4]
    鲁世平.奇摄动非线性时滞微分方程边值问题[J].数学研究与评论,2003,23(2):304-308.
    LU Shiping. Singularly perturbed boundary value problems for nonlinear differential equations with delay[J]. Journal of Mathematical Research and Exposition, 2003, 23(2):304-308.
    [5]
    ZHANG J F, ZHANG P A. Global asymptotic stability for a diffusion Lotka-Volterra competition system with time delays[J].Bull Korean Math Soc,2012,49(6):1255-1262.
    [6]
    SKRYNNIKOV Y. Solving initial value problem by matching asymptotic expansions[J].SIAM J Appl Math,2012,72(1): 405-416.
    [7]
    MO J Q, LIN W T, DU Z J. Singularly perturbed solution for nonlinear higher order elliptic equations with two parameters[J].J Sys Sci & Math,2013,33(2): 217-221.
    [8]
    MO J Q. Singularly perturbed reaction diffusion problem for nonlinear boundary condition with two parameters[J].Chin Phys,2010,19: 010203.
    [9]
    郑祖庥.泛函微分方程理论[M].合肥:安徽教育出版社,1994.
    [10]
    O’MALLEY JR R E. Introduction to Singular Perturbation[M]. New York: Academic Press, 1974.)
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