Oscillation of a logistic difference equation with several delays
Advances in Difference Equations volume 2006, Article number: 082143 (2006)
For a delay difference equation , g k (n) ≤ n, K > 0, a connection between oscillation properties of this equation and the corresponding linear equations is established. Explicit nonoscillation and oscillation conditions are presented. Positiveness of solutions is discussed.
Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht; 2000:viii+337.
Agarwal RP, Wong PJY: Advanced Topics in Difference Equations, Mathematics and Its Applications. Volume 404. Kluwer Academic, Dordrecht; 1997:viii+507.
Berezansky L, Braverman E: On oscillation of a logistic equation with several delays, fixed point theory with applications in nonlinear analysis. J. Comput. Appl. Math. 2000,113(1–2):255–265. 10.1016/S0377-0427(99)00260-5
Berezansky L, Braverman E: Oscillation properties of a logistic equation with several delays. J. Math. Anal. Appl. 2000,247(1):110–125. 10.1006/jmaa.2000.6830
Berezansky L, Braverman E, Liz E: Sufficient conditions for the global stability of nonautonomous higher order difference equations. J. Differ. Equations Appl. 2005,11(9):785–798. 10.1080/10236190500141050
Brauer F, Castillo-Chávez C: Mathematical Models in Population Biology and Epidemiology, Texts in Applied Mathematics. Volume 40. Springer, New York; 2001:xxiv+416.
Elaydi SN: An Introduction to Difference Equations, Undergraduate Texts in Mathematics. 2nd edition. Springer, New York; 1999:xviii+427.
Györi I, Ladas G: Oscillation Theory of Delay Differential Equations: With Applications, Oxford Mathematical Monographs. Oxford Science Publications.. The Clarendon Press Oxford University Press, New York; 1991:xii+368.
Kocić VL, Ladas G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications. Volume 256. Kluwer Academic, Dordrecht; 1993:xii+228.
Kot M: Elements of Mathematical Ecology. Cambridge University Press, Cambridge; 2001:x+453.
Levin SA, May RM: A note on difference-delay equations. Theoret. Population Biology 1976,9(2):178–187. 10.1016/0040-5809(76)90043-5
Luo J: Oscillation and linearized oscillation of a logistic equation with several delays. Appl. Math. Comput. 2002,131(2–3):469–476. 10.1016/S0096-3003(01)00159-X
Philos ChG: Oscillations in a nonautonomous delay logistic difference equation. Proc. Edinburgh Math. Soc. (2) 1992,35(1):121–131. 10.1017/S0013091500005381
Sun H-R, Li W-T: Qualitative analysis of a discrete logistic equation with several delays. Appl. Math. Comput. 2004,147(2):515–525. 10.1016/S0096-3003(02)00791-9
Yan JR, Qian CX: Oscillation and comparison results for delay difference equations. J. Math. Anal. Appl. 1992,165(2):346–360. 10.1016/0022-247X(92)90045-F
Zhou Y: Oscillation and nonoscillation for difference equations with variable delays. Appl. Math. Lett. 2003,16(7):1083–1088. 10.1016/S0893-9659(03)90098-X
Zhou Z, Zou X: Stable periodic solutions in a discrete periodic logistic equation. Appl. Math. Lett. 2003,16(2):165–171. 10.1016/S0893-9659(03)80027-7
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Berezansky, L., Braverman, E. Oscillation of a logistic difference equation with several delays. Adv Differ Equ 2006, 082143 (2006). https://doi.org/10.1155/ADE/2006/82143