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关于含双参数的非线性常微分方程的奇异摄动*

张汉林

张汉林. 关于含双参数的非线性常微分方程的奇异摄动*[J]. 应用数学和力学, 1989, 10(5): 453-461.
引用本文: 张汉林. 关于含双参数的非线性常微分方程的奇异摄动*[J]. 应用数学和力学, 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.

关于含双参数的非线性常微分方程的奇异摄动*

基金项目: * 中国科学院科学基金资助的课题

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

  • 摘要: 本文应用微分不等式方法研究含双小参数的非线性常微分方程的边值问题,作出渐近解并对余项进行估计.
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    [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.
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出版历程
  • 收稿日期:  1988-02-29
  • 刊出日期:  1989-05-15

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