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一类非线性奇异摄动自治微分系统的渐近解

冯依虎 陈怀军 莫嘉琪

冯依虎, 陈怀军, 莫嘉琪. 一类非线性奇异摄动自治微分系统的渐近解[J]. 应用数学和力学, 2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110
引用本文: 冯依虎, 陈怀军, 莫嘉琪. 一类非线性奇异摄动自治微分系统的渐近解[J]. 应用数学和力学, 2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110
FENG Yihu, CHEN Huaijun, MO Jiaqi. Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems[J]. Applied Mathematics and Mechanics, 2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110
Citation: FENG Yihu, CHEN Huaijun, MO Jiaqi. Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems[J]. Applied Mathematics and Mechanics, 2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110

一类非线性奇异摄动自治微分系统的渐近解

doi: 10.21656/1000-0887.380110
基金项目: 国家自然科学基金(11202106);安徽省教育厅自然科学重点基金(KJ2015A347;KJ2017A702);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520)
详细信息
    作者简介:

    冯依虎(1982—),男,副教授,硕士(E-mail: fengyihubzsz@163.com);莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

  • 中图分类号: O175.19

Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

Funds: The National Natural Science Foundation of China(11202106)
  • 摘要: 研究了一类广义Lienard奇异摄动系统.首先, 求出了系统的退化解;其次, 利用奇异摄动方法得到了系统的外部解,并用伸长变量方法, 求得了系统的初始层校正项;最后, 得到了系统解的任意次渐近解析展开式,并证明了解的一致有效性.该文所用的方法和理论, 具有广泛的实际应用价值.
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    [26] FENG Yihu, MO Jiaqi. Asymptotic solution for singularly perturbed fractional order differential equation[J]. J Math,2016,36(2): 239-245.
    [27] FENG Yihu, CHEN Xianfeng, MO Jiaqi. The generalized interior shock layer solution of a class of nonlinear singularly perturbed reaction diffusion problem[J]. Math Appl,2016,29(1): 161-165.
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出版历程
  • 收稿日期:  2017-04-25
  • 修回日期:  2017-06-07
  • 刊出日期:  2018-03-15

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