| Title:
|
Dynamic analysis of an impulsive differential equation with time-varying delays (English) |
| Author:
|
Li, Ying |
| Author:
|
Shao, Yuanfu |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
85-98 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
permanence |
| Keyword:
|
attractivity |
| Keyword:
|
impulse |
| Keyword:
|
delay |
| MSC:
|
34D20 |
| MSC:
|
34D23 |
| MSC:
|
34K13 |
| MSC:
|
34K45 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 06346374 |
| idMR:
|
MR3164578 |
| DOI:
|
10.1007/s10492-014-0043-9 |
| . |
| Date available:
|
2014-01-28T13:58:31Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143600 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Gaines, R. E., Mawhin, J. L.: Coincidence Degree, and Nonlinear Differential Equations.Lecture Notes in Mathematics 568 Springer, Berlin (1977). Zbl 0339.47031, MR 0637067, 10.1007/BFb0089537 |
| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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[7] Lakshmikantham, V., Bajnov, D. D., Simeonov, P. S.: Theory of Impulsive Differential Equations.Series in Modern Applied Mathematics 6 World Scientific, Singapore (1989). Zbl 0719.34002, MR 1082551 |
| Reference:
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[8] Liu, X., Takeuchi, Y.: Periodicity and global dynamics of an impulsive delay Lasota-Wazewska model.J. Math. Anal. Appl. 327 (2007), 326-341. Zbl 1116.34063, MR 2277416, 10.1016/j.jmaa.2006.04.026 |
| Reference:
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| Reference:
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| Reference:
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[11] Shao, Y., Dai, B., Luo, Z.: The dynamics of an impulsive one-prey multi-predators system with delay and Holling-type II functional response.Appl. Math. Comput. 217 (2010), 2414-2424. Zbl 1200.92044, MR 2733684, 10.1016/j.amc.2010.07.042 |
| Reference:
|
[12] Shao, Y., Li, Y., Xu, C.: Periodic solutions for a class of nonautonomous differential system with impulses and time-varying delays.Acta Appl. Math. 115 (2011), 105-121. Zbl 1247.34121, MR 2812979, 10.1007/s10440-010-9598-y |
| Reference:
|
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| . |
