A trichotomy result for non-autonomous rational difference equations

 Access to full text

 Full (PDF)

1. [1] Camouzis E., Ladas G., When does periodicity destroy boundedness in rational equations?, J. Difference Equ. Appl., 2006, 12(9), 961–979 http://dx.doi.org/10.1080/10236190600822369 Zbl1112.39003
2. [2] Camouzis E., Ladas G., Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Adv. Discrete Math. Appl., 5, Chapman & Hall/CRC Press, Boca Raton, 2007 http://dx.doi.org/10.1201/9781584887669 Zbl1129.39002
3. [3] Cushing J.M., Henson S.M., A periodically forced Beverton-Holt equation, J. Difference Equ. Appl., 2002, 8(12), 1119–1120 http://dx.doi.org/10.1080/1023619021000053980 Zbl1023.39013
4. [4] Elaydi S., Sacker R.J., Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures, J. Difference Equ. Appl., 2005, 11(4–5), 337–346 http://dx.doi.org/10.1080/10236190412331335418 Zbl1084.39005
5. [5] El-Metwally H.A., Grove E.A., Ladas G., A global convergence result with applications to periodic solutions, J. Math. Anal. Appl., 2000, 245(1), 161–170 http://dx.doi.org/10.1006/jmaa.2000.6747 Zbl0971.39004
6. [6] Grove E.A., Kostrov Y., Ladas G., Schultz S.W., Riccati difference equations with real period-2 coefficients, Comm. Appl. Nonlinear Anal., 2007, 14(2), 33–56 Zbl1126.39001
7. [7] Grove E.A., Ladas G., Periodicities in Nonlinear Difference Equations, Adv. Discrete Math. Appl., 4, Chapman & Hall/CRC Press, Boca Raton, 2005 Zbl1078.39009
8. [8] Grove E.A., Ladas G., Predescu M., Radin M., On the global character of the difference equation $x_{n+1}=\frac{\alpha +\gamma x_n-(2k+1)+\delta x_{n-2l}}{A+x_{n-2l}}$ , J. Difference Equ. Appl., 2003, 9(2), 171–199 http://dx.doi.org/10.1080/1023619021000054015 Zbl1038.39004
9. [9] Karakostas G.L., Stević S., On the recursive sequence $x_{n+1}=B+\frac{x_{n-k}}{a_0{x}_n+\cdots +a_{k-1}{x}_{n-k+1}+\gamma }$ , J. Difference Equ. Appl., 2004, 10(9), 809–815 http://dx.doi.org/10.1080/10236190410001659732 Zbl1068.39012
10. [10] Kocić V.L., Ladas G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Math. Appl., 256, Kluwer, Dordrecht, 1993 Zbl0787.39001
11. [11] Kulenovic M.R.S., Merino O., Stability analysis of Pielou’s equation with period-two coefficient, J. Difference Equ. Appl., 2007, 13(5), 383–406 http://dx.doi.org/10.1080/10236190601045929 Zbl1123.39004
12. [12] Palladino F.J., Difference inequalities, comparison tests, and some consequences, Involve, 2008, 1(1), 91–100 http://dx.doi.org/10.2140/involve.2008.1.91 Zbl1154.39012
13. [13] Palladino F.J., On the characterization of rational difference equations, J. Difference Equ. Appl., 2009, 15(3), 253–260 http://dx.doi.org/10.1080/10236190802119903 Zbl1169.39005
14. [14] Palladino F.J., On periodic trichotomies, J. Difference Equ. Appl., 2009, 15(6), 605–620 http://dx.doi.org/10.1080/10236190802258677 Zbl1207.39018
15. [15] Stevic S., Behavior of the positive solutions of the generalized Beddington-Holt equation, Panamer. Math. J., 2000, 10(4), 77–85 Zbl1039.39005
16. [16] Stevic S., On the recursive sequence x n+1 = α n + x n−1/x n. II, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 2003, 10(6), 911–916 
17. [17] Stevic S., A short proof of the Cushing-Henson conjecture, Discrete Dyn. Nat. Soc., 2006, ID 37264 Zbl1149.39300
18. [18] Stevic S., On positive solutions of a (k + 1)th order difference equation, Appl. Math. Lett., 2006, 19(5), 427–431 http://dx.doi.org/10.1016/j.aml.2005.05.014 Zbl1095.39010