Title:
|
Periodic solutions for a class of functional differential system (English) |
Author:
|
Wang, Weibing |
Author:
|
Lai, Baishun |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
48 |
Issue:
|
2 |
Year:
|
2012 |
Pages:
|
139-148 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results. (English) |
Keyword:
|
functional differential equation |
Keyword:
|
periodic solution |
Keyword:
|
fixed point theorem |
MSC:
|
34K13 |
idMR:
|
MR2946213 |
DOI:
|
10.5817/AM2012-2-139 |
. |
Date available:
|
2012-06-08T08:35:45Z |
Last updated:
|
2013-09-19 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142827 |
. |
Reference:
|
[1] A. Wan, D. Jiang, Xu, X.: A new existence theory for positive periodic solutions to functional differential equations.Comput. Math. Appl. 47 (2004), 1257–1262. MR 2070981, 10.1016/S0898-1221(04)90120-4 |
Reference:
|
[2] Cheng, S., Zhang, G.: Existence of positive periodic solutions for non-autonomous functional differential equations.Electron. J. Differential Equations 59 (2001), 1–8. Zbl 1003.34059, MR 1863778 |
Reference:
|
[3] Chow, S.: Existence of periodic solutions of autonomous functional differential equations.Differential Equations 15 (1974), 350–378. Zbl 0295.34055, MR 0336003, 10.1016/0022-0396(74)90084-9 |
Reference:
|
[4] Freedman, H. I., Wu, J.: Periodic solutions of single–species models with periodic delay.SIAM J. Math. Anal. 23 (1992), 689–701. Zbl 0764.92016, MR 1158828, 10.1137/0523035 |
Reference:
|
[5] Wang, H: Positive periodic solutions of functional differential equations.J. Differential Equations 202 (2004), 354–366. Zbl 1064.34052, MR 2069005, 10.1016/j.jde.2004.02.018 |
Reference:
|
[6] Jiang, D., Wei, J., Zhang, B.: Positive periodic solutions of functional differential equations and population models.Electron. J. Differential Equations 71 (2002), 1–13. Zbl 1010.34065, MR 1921144 |
Reference:
|
[7] Joseph, W., So, H., Yu, J.: Global attractivity and uniform persistence in Nicholson’s blowflies.Differential Equations Dynam. Systems 1 (1994), 11–18. MR 1386035 |
Reference:
|
[8] Kuang, Y., Smith, H. L.: Periodic solutions of differential delay equations with threshold-type delays, oscillations and dynamics in delay equations.Contemp. Math. 129 (1992), 153–176. MR 1174140, 10.1090/conm/129/1174140 |
Reference:
|
[9] Li, Z., Wang, X.: Existence of positive periodic solutions for neutral functional differential equations.Electron. J. Differential Equations 34 (2006), 1–8. Zbl 1099.34063, MR 2213578 |
Reference:
|
[10] Weng, P., Liang, M.: The existence and behavior of periodic solution of hematopoiesis model.Math. Appl. 4 (1995), 434–439. MR 1356679 |
. |