On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay

Huang Xiankai; Dong Qinxi

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(8): 847-850

Huang Xiankai, Dong Qinxi. On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay[J]. Applied Mathematics and Mechanics, 1999, 20(8): 847-850.

Citation:

Huang Xiankai, Dong Qinxi. On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay[J]. Applied Mathematics and Mechanics, 1999, 20(8): 847-850.

Citation:

Huang Xiankai, Dong Qinxi. On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay[J]. Applied Mathematics and Mechanics, 1999, 20(8): 847-850.

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On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay

Huang Xiankai¹,
Dong Qinxi²

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 Date: 1998-04-23
Rev Recd Date: 1999-02-07
Publish Date: 1999-08-15

Abstract

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)=gradG(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 populat ion model is proved.
- delay,
- periodic solution,
- existence,
- coincidence degree

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References(2)

References

[1]	Gaines R E,Mawhin J L.Coincidence degree and nonlinear differential equations[A].Lecture Notes in Math[C],567,Berlin:Springer-Verlag,1977.
[2]	Gopalsamy K.Stability and Oscillations in Delay Differential Equations of Population Dynamics[M].Boston:Kluwer Academic Publisher,1992,