Existence and global attractivity of positive periodic solution of an impulsive delay differential equation

International Journal of Phytoremediation

Volumn 83, Issue 12, 2004, Pages 1279-1290

  Huo, Hai Feng ^a   Li, Wang Tong ^b   Liu, Xinzhi ^c  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

^b LANZHOU UNIVERSITY   (China)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

2000 AMS Subject Classifications; 34K20; 92D25; Global attractivity; Impulsive delay differential equation; Periodic solution

Indexed keywords

EID: 85014299018     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810410001724599     Document Type: Article

References (25)

1. Bainov DD, Simeonov PS, 1989 Systems with impulse effect, theory and applications Ellis Horwood Series in Mathematics and its Applications, Ellis Horwood Chichister
2. Ballinger, G, and Liu, X. 1999. Existence and uniqueness results for impulsive delay differential equations. Dynam. Contin. Discrete Impuls. Systems, 5: 579–591.
3. Gopalsamy K, 1992 Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic Dordrecht
4. Gopalsamy, K, and Trofimchuk, SI. 1999. Almost periodic solutions of Lasota-Wazewska type delay differential equations. J. Math. Anal. Appl., 237: 106–127.
5. Gopalsamy, K, and He, XZ. 1991. Global attractivity and oscillations in periodic logistic integrodifferential equation. Houston J. Math., 17: 157–177.
6. Gopalsamy, K, and He, XZ. 1997. Oscillation and convergence in almost periodic competition system. Acta Appl. Math., 46: 247–266.
7. Gopalsamy, K, Kulenovic, MRS, and Ladas, G. 1990. Environmental periodicity and time delays in a ‘Food Limited' population model. J. Math. Anal. Appl., 147: 545–555.
8. Gopalsamy, K, and Zhang, BG. 1989. On the delay differential equations with impulses. J. Math. Anal. Appl., 139: 110–112.
9. Graef, JR, Qian, C, and Spikes, PW. 1996. Oscillation and global attractivity in a periodic delay equation. Canad. Math. Bull., 39: 275–283.
10. Gyori I, Ladas G, 1991 Oscillation Theory of Delay Differential Equations with Applications, Clarendon Oxford
11. Krasnoselskii MA, 1964 Positive Solutions of Operator Equations, Gorninggen Noordhoff
12. Kuang Y, 1993 Delay Differential Equations with Applications in Population Dynamics, Academic Press Boston
13. Kulenovic, MRS, and Ladas, G. 1987. Linearized oscillation in population dynamics. Bull. Math. Biol., 44: 615–627.
14. Kulenovic, MRS, Ladas, G, and Sficas, YS. 1989. Global attractivity in population dynamics. Computers Math. Applic., 18: 925–928.
15. Ladas, G, Sficas, YG, and Stavroulakis, IP. 1983. Asymptotic behavior of solutions of retarded differential equations. Proc. Amer. Math. Soc., 88: 247–253.
16. Lakshmikantham V, Bainov DD, Simenov PS, 1989 Theory of Impulsive Differential Equations, World Scientific Singapore
17. Liu, X, and Ballinger, G. 2002. Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal., 51: 633–647.
18. Liu, X, and Ballinger, G. 2001. Uniform asymptotic stability of impulsive delay differential equations. Computers Math. Appl., 41: 903–915.
19. Liu, X, and Ballinger, G. 2003. Boundedness for impulsive delay differential equations and applications to population growth models. Nonlinear Anal., 53: 1041–1062.
20. Saker SH, Agarwal S, Oscillation and global attractivity of a periodic survival red blood cells model Computers Math. Applic (in press)
21. Shen JH, 1997 Global existence and uniqueness, oscillation and nonoscillation of impulsive delay differential equations Acta Math. Sinica 40 1 53 59 (in Chinese)
22. Yan, JR, and Zhao, AM. 1998. Oscillation and stability of linear impulsive delay differential equations. J. Math. Anal. Appl., 227: 187–194.
23. Yan, JR. 2003. Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model. J. Math. Anal. Appl., 279: 111–120.
24. Zhang, BG, and Liu, YJ. 2003. Global attractivity for certain impulsive delay differential equations. Nonlinear Analysis, 35: 725–736.
25. Zhang, XS, and Yan, JY. 1998. Global attractivity in impulsive functional differential equation. Indian J. Pure Appl. Math., 29: 871–878.