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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (8): 908-911.

• 论文 • 上一篇    下一篇

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY

黄先开1, 董勤喜2   

  1. 1. Department of Mathematics, Beijing Institute of Business, Beijing 100037, P R China;
    2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P R China
  • 收稿日期:1998-04-23 修回日期:1999-02-07 出版日期:1999-08-18 发布日期:1999-08-18

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY

Huang Xiankai1, Dong Qinxi2   

  1. 1. Department of Mathematics, Beijing Institute of Business, Beijing 100037, P R China;
    2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P R China
  • Received:1998-04-23 Revised:1999-02-07 Online:1999-08-18 Published:1999-08-18

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摘要： In this paper, higher dimensional periodic systems with delay of the form
x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)),
x′(t)= grad G(x(t))+f(t,x(t-τ))
are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.

关键词: delay, existence, coincidence degree, periodic solution

Abstract: In this paper, higher dimensional periodic systems with delay of the form
x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)),
x′(t)= grad G(x(t))+f(t,x(t-τ))
are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.

Key words: delay, periodic solution, existence, coincidence degree

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