您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

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

PDF (PC)

963

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
[1] JUAN J Nieto, YU Jiang, YAN Jurang. Monotone iterative method for functional-differential equations[J]. Nonlinear Analysis, 1998, 32(6):741-747.
[2] JIANG Daqing, WEI Junjie. Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations[J]. Nonlinear Analysis. 2002, 50(7): 885-898.
[3] JIANG Daqing, JUAN J Nieto, ZUO Wenjie. On monotone method for first and second-order periodic boundary value problems and periodic solutions of functional differential equations[J]. Journal of Mathematical Analysis and Applications. 2004, 289(2): 691-699.
[4] WU Yuexiang. Existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter[J]. Nonlinear Analysis, 2009, 70(1): 433-443.
[5] WANG Youyu, LIAN Hairong, GE Weigao. Periodic solutions for a second order nonlinear functional differential equation[J]. Applied Mathematics Letters, 2007, 20(1): 110-115.
[6] LI Qiang, LI Yongxiang. Existence and multiplicity of positive periodic solutions for second-order functional differential equations with infinite delay[J]. Electronic Journal of Differential Equations, 2014(93): 1-14.
[7] CABADA A. The method of lower and upper solutions for second, third, fourth and higher order boundary value problem[J]. Journal of Mathematical Analysis and Applications, 1994, 185(2): 302-320.
[8] JUAN J Nieto. Nonlinear second-order periodic boundary value problems[J]. Journal of Mathematical Analysis and Applications, 1988, 130(1): 22-29.
[9] PEDRO J Torres. Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem[J]. J Differential Equations, 2003, 190(2):643-662.
[10] LI Yongxiang. Positive periodic solutions for fully third-order ordunary differenttial equations[J]. Computers and Mathematics with Applications, 2010, 59(11): 3461-3471.
[11] CHU Jifeng, ZHOU Zhongcheng. Positive solutions for singular non-linear third-order periodic boundary value problems[J]. Nonlinear Analysis, 2006, 64(7):1528-1542.
[12] GUO Dajun, LIU Xinzhi. Extremal solutions for a boundary value problem of nth-order impulsive integro-differential equations in a banach space[J]. Mathematical Analysis, 2006, 13(5): 599-619.
[13] HANS Peter Heinz. On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions[J]. Nonlinear Analysis, 1983, 7(12):1351-1371.
[1] 董颖,吕云飞. 具有周期感染率的年龄结构传染病模型的阈值动力学分析[J]. 《山东大学学报(理学版)》, 2025, 60(4): 50-59.
[2] 许一诺,刘利斌,杨秀. 带时滞项的二阶奇异摄动问题的自适应移动网格算法[J]. 《山东大学学报(理学版)》, 2025, 60(12): 84-93.
[3] 喜霞,李永祥. 一类含导数项的二阶时滞微分方程的周期解[J]. 《山东大学学报(理学版)》, 2025, 60(12): 103-109.
[4] 范建航,吴奎霖. 一类非自治分段双线性系统周期解[J]. 《山东大学学报(理学版)》, 2024, 59(12): 114-121.
[5] 苌庆,亓庆源,刘志强. 含有乘性噪声的理性期望模型的最优控制[J]. 《山东大学学报(理学版)》, 2022, 57(11): 50-57.
[6] 刘志强,亓庆源,苌庆. 具有非对称信息控制器平均场系统的分散控制[J]. 《山东大学学报(理学版)》, 2022, 57(11): 58-69.
[7] 王苗苗,丁小丽,李佳敏. 分数阶随机时滞微分方程的波形松弛方法[J]. 《山东大学学报(理学版)》, 2022, 57(1): 101-110.
[8] 王琪,贾建文. 具有公众健康教育影响的随机传染病模型的非平凡周期解[J]. 《山东大学学报(理学版)》, 2021, 56(9): 28-34.
[9] 赵娇. 一类非线性三阶差分方程正周期解的存在性和多解性[J]. 《山东大学学报(理学版)》, 2021, 56(9): 50-58.
[10] 马德青,胡劲松. 消费者参考质量存在时滞效应的动态质量改进策略[J]. 《山东大学学报(理学版)》, 2020, 55(9): 101-89.
[11] 王爱丽. 具有脉冲控制和病毒感染的害虫治理模型的分支分析[J]. 《山东大学学报(理学版)》, 2020, 55(7): 1-8.
[12] 杨虎军,韩晓玲. 一类非自治四阶常微分方程正周期解的存在性[J]. 《山东大学学报(理学版)》, 2020, 55(6): 109-114.
[13] 陈瑞鹏,李小亚. 带阻尼项的二阶奇异微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(8): 33-41.
[14] 张申贵. 变分方法对变指数脉冲微分系统的应用[J]. 《山东大学学报(理学版)》, 2019, 54(4): 22-28.
[15] 章欢,李永祥. 含时滞导数项的高阶常微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(4): 29-36.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发