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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 665-671.doi: 10.3969/j.issn.1005-3085.2022.04.014

• • 上一篇    下一篇

带状态依赖时滞微分方程的周期与几乎周期解的应用

周  辉,   王  文   

  1. 合肥师范学院数学与统计学院，合肥 230601
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 基金资助:
    国家自然科学基金 (12001152)；安徽省自然科学基金 (2008085QA08)；安徽高校自然科学基金 (KJ2021ZD0112).

Applications to Periodic and Almost Periodic State-dependent Delayed Differential Equations

ZHOU Hui,   WANG Wen   

  1. School of Mathematics and Statistics, Hefei Normal University, Hefei 230601
  • Online:2022-08-15 Published:2022-10-15
  • Supported by:
    The National Natural Science Foundation of China (12001152); the Natural Science Foundation of Anhui Province (2008085QA08); the Key Project of Anhui Higher Education (KJ2021 ZD0112).

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摘要：

周期或几乎周期现象普遍存在于自然界中，而借助微分方程可更好地描述这些现象的动力学行为。而时滞效应常常伴随在一些实际系统中，将分别研究一类带有状态依赖时滞的周期驱动的微分方程和几乎周期驱动的微分方程。利用Schauder不动点定理，分别建立所研究方程的周期解与几乎周期解的存在性判据。同时，最后给出两个例子一一例证文中所得到的主要结果的可行性。

关键词: 状态依赖时滞, 周期解, 几乎周期解, Schauder 不动点定理

Abstract:

The periodic or almost periodic phenomena are commonly found in the natural world. And some real systems usually contain the effects of time delays, differential equations with delay depending on state forced by periodicity and almost periodicity are investigated, respectively. By Schauder's fixed point theorem, the criteria of the existence of periodic and almost periodic solutions to the equations are shown. Finally, two examples will be given to illustrate the effectiveness of the main results.

Key words: state-dependent delay, periodic solution, almost periodic solution, Schauder's fixed point theorem

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