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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (4): 413-422    
    
一类具有不连续源的奇摄动半线性微分方程组边值问题
包立平
杭州电子科技大学理学院, 浙江杭州310018
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
 全文: PDF 
摘要： 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
    
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
收稿日期: 2016-08-14 出版日期: 2018-12-01
CLC:  O175.14  
基金资助: 国家自然科学基金(51775154)
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包立平

引用本文:

包立平. 一类具有不连续源的奇摄动半线性微分方程组边值问题[J]. 高校应用数学学报, 2017, 32(4): 413-422.

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.

链接本文:

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

[1] 包立平. 一类奇摄动半线性时滞抛物型偏微分方程的渐近解[J]. 高校应用数学学报, 2016, 31(3): 307-315.
[2] 李惠芳, 包立平. 多尺度高维亚式期权定价的奇摄动解[J]. 高校应用数学学报, 2015, 30(4): 389-398.
[3] 陈雯, 姚静荪, 孙国正. 一个奇摄动微分方程非线性混合边值问题[J]. 高校应用数学学报, 2015, 30(1): 117-126.