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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 413-422    DOI:
    
A class of boundary value problem of singular perturbed semi-linear differential systems with discontinuous source term
BAO Li-ping
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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Abstract  In this paper a class of boundary value problems of the singular perturbed semi-linear differential systems with discontinuous source term is discussed. The formal asymptotic expansion is constructed. Using Hartman-Nagumo inequality, the existence and uniqueness of the solution of the singular perturbed semi-linear differential systems is proved. Using Aumann intermediate theorem, the smoothness of the solution of the systems is obtained. And the uniformly valid estimation for the solution of the systems is obtained.

Key words： singular perturbation      semi-linear differential systems      Hartman-Nagumo inequality      discontinuous source term      Aumann intermediate theorem
     
Received: 14 August 2016      Published: 01 December 2018
CLC:  O175.14  
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BAO Li-ping. A class of boundary value problem of singular perturbed semi-linear differential systems with discontinuous source term. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 413-422.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I4/413


一类具有不连续源的奇摄动半线性微分方程组边值问题

讨论了一类具有不连续源的奇摄动半线性微分方程组边值问题, 构造了形式渐近解. 利用Hartman-Nagumo不等式证明了奇摄动半线性微分方程组的解的存在性与唯一性, 利用Aumann介值定理, 得到了该方程组解的光滑性, 并且得到了一致有效估计.

关键词： 奇摄动,  半线性微分方程组,  Hartman-Nagumo不等式,  不连续源,  Aumann介值定理
 
[1] BAO Li-ping. The asymptotic solution of a class of singular perturbed semi-linear delayed parabolic partial differential equation[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 307-315.
[2] LI Hui-fang, BAO Li-ping. Solution to multiscale Asian option pricing model with the singular perturbation method[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 389-398.
[3] CHEN Wen, YAO Jing-sun, SUN Guo-zheng. A nonlinear mixed boundary value problem for singularly perturbed differential equation[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(1): 117-126.