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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (06): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.585

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带双参数的脉冲泛函微分方程正周期解的存在性

徐嫚   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2014-12-26 修回日期:2015-05-20 出版日期:2015-06-20 发布日期:2015-07-31
  • 作者简介:徐嫚(1989-),女,硕士研究生,研究方向为常微分方程边值问题.E-mail:xmannwnu@126.com
  • 基金资助:
    国家自然科学基金资助项目(11361054);甘肃省自然科学基金资助项目(1208RJZA258)

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

XU Man   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2014-12-26 Revised:2015-05-20 Online:2015-06-20 Published:2015-07-31

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摘要： 研究了带双参数的脉冲泛函微分方程 u'(t)=h(t,u(t))-λf(t,u(t-τ(t))), t∈R, t≠tk, u(t+k)-u(tk)=μIk(tk,u(tk-τ(tk))) 正周期解的存在性, 其中λ>0, μ≥0为参数, 获得了其在更一般条件下正周期解的存在性结果。主要结果的证明基于不动点指数理论。

关键词: 脉冲泛函微分方程, 双参数, 正周期解, 不动点指数

Abstract: We study the existence of positive periodic solutions of impulsive functional differential equations with two parameters u'(t)=h(t,u(t))-λf(t,u(t-τ(t))), t∈R, t≠tk, u(t+k)-u(tk)=μIk(tk,u(tk-τ(tk))), where λ>0, μ≥0 are parameters and show the existence results of positive periodic solutions in more general conditions. The proof of the main results is based on the fixed point index theory.

Key words: Impulsive functional differential equations, two parameters, positive periodic solutions, fixed point index

中图分类号: 

  • O175.8
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