On the number of positive periodic solutions of functional differential equations and population models

Mathematical Models and Methods in Applied Sciences

Volumn 15, Issue 4, 2005, Pages 555-573

  Jiang, Daqing ^a   O'Regan, Donal ^b   Agarwal, Ravi P ^c   Xiaojie, X U ^a  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c Florida Institute of Technology   (United States)

Author keywords

Functional differential equation; Population models; Positive periodic solution

Indexed keywords

EID: 17144363669     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202505000467     Document Type: Article

References (22)

1. T. A. Burton, Volterra Integral and Differential Equations (Academic Press, 1983).
2. T. A. Burton and B. Zhang, Uniform ultimate boundedness and periodicity in functional differential equations, Tohoku Math. J. 42 (1990) 93-100.
3. M. Cavani, M. Lizana and H. L. Smith, Stable periodic orbits for a predator-prey model with delay, J. Math. Anal. Appl. 249 (2000) 324-339.
4. S.-N. Chow, Existence of periodic solutions of autonomous functional differential equations, J. Diff. Eqns. 15 (1974) 350-378.
5. J. M. Cushing, Integra-Differential Equations with Delay Models in Population Dynamics, Lecture Notes in Biomath., Vol. 20 (Springer-Verlag, 1977).
6. K. Deimling, Nonlinear Functional Analysis (Springer-Verlag, 1985).
7. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics (Kluwer, 1992).
8. K. Hadeler, On the stability of the stationary state of a population growth equation with time-lag, J. Math. Biol 3 (1976) 197-201.
9. L. Hatvani and T. Krisztin, On the existence of periodic solutions for linear inhomogeneous and quasilinear functional differential equations, J. Diff. Eqns. 97 (1992) 1-15.
10. Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay (Springer-Verlag, 1991).
11. M. A. Krasnoselskii, Positive Solutions of Operator Equations (Noordhoff, 1964).
12. Y. Kuang, Delay Differential Equations with Application in Population Dynamics (Academic Press, 1993).
13. G. Makay, Periodic solutions of dissipative functional differential equations, Tohoku Math. J. 46 (1994) 417-426.
14. R. M. May, Stability and Complexity in Model Ecosystems (Princeton Univ. Press, 1973).
15. R. M. May and W. J. Leonard, Nonlinear aspect of competition between three species, SIAM J. Appl. Math. 29 (1975) 243-253.
16. H. L. Royden, Real Analysis (Macmillan, 1988).
17. W. Stech, The effect of time lags on the stability of the equilibrium state of a population growth equation, J. Math. Biol. 5 (1978) 115-120.
18. M. Wazewska-Czyzewska and A. Lasota, Mathematical models of the red cell system, Mat. Stosowana 6 (1976) 25-40.
19. P. Weng and M. Liang, The existence and behavior of periodic solutions of a hematopoiesis model, Math. Appl. 8 (1995) 434-439.
20. D. Q. Jiang, J. Wei and B. Zhang, Positive periodic solutions of functional differential equations and population models, Electronic J. Diff. Eqns. 71 (2002) 1-13.
21. D. Q. Jiang and J. J. Wei, Existence of positive periodic solutions for Volterra integro-differential equations, Acta Math. Sci. 21B (2002) 553-560.
22. W. S. C. Gurney, S. P. Blythe and R. M. Nisbet, Nicholson's blowfies revisited, Nature 287 (1980) 17-20.