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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (8): 84-94.doi: 10.6040/j.issn.1671-9352.0.2017.582

• • 上一篇    

一类三阶时滞微分方程在Banach空间中的周期解的存在性

陈雨佳, 杨和*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2017-11-14 出版日期:2018-08-20 发布日期:2018-07-11
  • 作者简介:陈雨佳(1993— ), 女, 硕士研究生, 研究方向为非线性泛函分析. E-mail: 13919241816@163. com*通信作者简介: 杨和(1982— ), 男, 博士, 副教授, 硕士生导师, 研究方向为非线性泛函分析. E-mail: yanghe256@163.com
  • 基金资助:
    国家基金委青年基金科学资助项目(11701457);甘肃省科技计划资助项目(17JR5RA071)

Existence of periodic solutions of a class of third order delay differential equations in Banach spaces

CHEN Yu-jia, YANG He*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-11-14 Online:2018-08-20 Published:2018-07-11

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摘要： 利用上下解单调迭代方法, 考虑有序Banach空间E中三阶时滞微分方程u(t)+M0u(t-τ0)=f(t,u(t), u(t-τ1), u(t-τ2)),〓t∈R,2π-周期解的存在性, 其中 f: R×E3→E 连续, 关于 t 以 2π-为周期, τ0,τ1,τ2为正常数。 通过建立新的极大值原理和构造方程 2π-周期解的单调迭代求解程序, 得到了该方程 2π-周期解的存在性与唯一性结果。

关键词: 有序Banach空间, 周期解, 时滞微分方程, 极大值原理, 单调迭代方法

Abstract: Applying the monotone iterative method of upper and lower solutions, we discuss the existence of 2π-periodic solutions for the third-order differential equation with delays in ordered Banach space Eu(t)+M0u(t-τ0)=f(t,u(t), u(t-τ1), u(t-τ2)), t∈R,where f:R×E3→E is a continuous function which is 2π-periodic in t, and τ0,τ1,τ2 are positive constants. By establishing a new maximum principle, a monotone iterative procedure for the equation is constructed. Some existence and uniqueness results of 2π-periodic solutions for this equation are obtained.

Key words: ordered Banach space, differential equation with delays, monotone iterative technique, maximum principle, periodic solution

中图分类号: 

  • O175.15
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