Optimal existence theory for single and multiple positive periodic solutions to functional difference equations

Applied Mathematics and Computation

Volumn 161, Issue 2, 2005, Pages 441-462

  Jiang, Daqing ^a   O'Regan, Donal ^b   Agarwal, R P ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c Florida Institute of Technology ^*  (United States)

Author keywords

Fixed point theorem in cones; Functional difference equation; Positive periodic solution

Indexed keywords

FUNCTION EVALUATION; MATHEMATICAL MODELS; THEOREM PROVING; TOPOLOGY;

BIOMATHEMATICAL MODELS; FIXED POINT THEOREM IN CONES; FUNCTIONAL DIFFERENCE EQUATION; POSITIVE PERIODIC SOLUTION;

DIFFERENCE EQUATIONS;

EID: 10044298643     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.12.097     Document Type: Article

References (22)

1. W.G. Kelley, A.C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, New York, 1991.
2. Y.K. Li, Existence and global attractivity of positive periodic solution for a class of delay differential equations, Sci. China (Series A) 28 (1998) 108-118 (in Chinese).
3. R.Y. Zhang, Z.C. Wang, Y. Cheng, J. Wu, Periodic solutions of a single species discrete population model with periodic harvest/stock, Comput. Math. Appl. 39 (2000) 77-90.
4. D.Q. Jiang, R.P. Agarwal, Existence of positive solutions for a class of difference equations with several deviating arguments, Advance in Difference Equation IV of the J. Comput. Math. Appl. 45 (2003) 1303-1309.
5. D.Q. Jiang, J.J. Wei, Existence of positive periodic solution for nonautonomous delay differential equations, Chin. Ann. Math. (Series A) 20A (1999) 716-720 (in Chinese).
6. D.Q. Jiang, J. Wei, B. Zhang, Positive periodic solutions of functional differential equations and population models, Electron. J. Differ. Equal. 2002 (71) (2002) 1-13.
7. Y. Kuang, Global stability for a class of nonlinear nonautonomous delay logistic equations, Nonlinear Anal. 17 (1991) 627-634.
8. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, 1992.
9. K. Gopalsamy, B.S. Lalli, Oscillatory and asymptotic behavior of a multiplicative delay logistic equation, Dynam. Stability Syst. 7 (1992) 35-42.
10. B.C. Pielou, Mathematics Ecology, Wiley-Interscience, New York, 1977.
11. S. Lenhart, C. Travis, Global stability of a biological model with time delay, Proc. Amer. Math. Soc. 96 (1986) 75-78.
12. J. Mallet-Paret, R. Nussbaum, Global continuation and asymptotic behavior for periodic solutions of a differential-delay equation, Ann. Math. Pure. Appl. 145 (1986) 33-128.
13. J. Luo, J. Yu, Global asymptotic stability of nonautonomous mathematical ecological equations with distributed deviating arguments, Acta Math. Sin. 41 (1998) 1273-1282 (in Chinese).
14. P. Weng, M. Liang, The existence and behavior of periodic solution of Hematopoiesis model, Math. Appl. 8 (4) (1995) 434-439.
15. P. Weng, Existence and global attractivity of periodic solution of integrodifferential equation in population dynamics, Acta Appl. Math. 12 (4) (1996) 427-434.
16. W.S.C. Gurney, S.P. Blythe, R.M. Nisbet, Nicholson's blowfies revisited, Nature 287 (1980) 17-20.
17. K. Gopalsamy, P. Weng, Global attractivity and level crossing in model of Hoematcpoiesis, Bull. Inst. Math., Acad. Sin. 22 (4) (1994) 341-360.
18. W. Joseph, H. So, J. Yu, Global attractivity and uniformly persistence in Nicholson's blowfies, Differ. Equal. Dynam. Syst. 2 (1) (1994) 11-18.
19. M.C. Mackey, Galass, Oscillations and chaos in phycological control systems, Sciences 197 (2) (1987) 287-289.
20. D.Q. Jiang, J.J. Wei, Existence of positive periodic solutions for Volterra integro-differential equations, Acta Math. Sci. 21B (4) (2002) 553-560.
21. A.Y. Wan, D.Q. Jiang, Existence of positive periodic solutions for functional differential equations, Kyushu J. Math. 56 (1) (2002) 193-202.
22. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, New York, 1985.