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The oscillatory character of the recursive sequence \(x_{n+1}= \frac {\alpha+\beta x_{n-k+1}}{A+Bx_{n-2k+1}}\). (English) Zbl 1094.39006
A difference equation in rational form and with positive parameters and initial conditions is considered. Conditions are given for the boundedness, oscillatory behavior and stability of the orbit of the difference equation.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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[1] Dehghan, M.; Saadatmandi, A., Bounds for solutions of a six-point partial-difference scheme, Computers and mathematics with applications, 47, 83-89, (2004) · Zbl 1054.65094
[2] M. Dehghan, M. Jaberi Douraki, On the recursive sequence \(x_{n + 1} = \frac{\alpha + \beta x_{n - k + 1} + \gamma x_{n - 2 k + 1}}{\mathit{Bx}_{n - k + 1} + \mathit{Cx}_{n - 2 k + 1}}\), Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2005.01.004. · Zbl 1090.39006
[3] DeVault, R.; Kosmala, W.; Ladas, G.; Schaultz, S.W., Global behavior of \(y_{n + 1} = \frac{p + y_{n - k}}{\mathit{qy}_n + y_{n - k}}\), Nonlinear analysis, theory, methods and applications, 47, 4743-4751, (2001) · Zbl 1042.39523
[4] Gibbons, C.H.; Kulenovic, M.R.S.; Ladas, G., On the recursive sequence \(x_{n + 1} = \frac{\alpha + \beta x_n}{\gamma + x_n}\), Mathematical sciences research hot-line, 4, 2, 1-11, (2000) · Zbl 1039.39004
[5] Franke, J.E.; Hong, J.T.; Ladas, G., Global attractivity and convergence to the two-cycle in a difference equation, Journal of difference equations and applications, 5, 2, 203-209, (1999) · Zbl 0927.39005
[6] Jaroma, J.H., On the global asymptotic stability of \(x_{n + 1} = \frac{\alpha + \beta x_n}{A + \mathit{Cx}_{n - 1}}\), (), 281-294
[7] Kocic, V.L.; Ladas, G., Global asymptotic behavior of nonlinear difference equations of higher order with applications, (1993), Kluwer Academic Publishers Dordrect · Zbl 0787.39001
[8] Kocic, V.L.; Ladas, G., Global attractivity in nonlinear delay difference equations, Proceedings of American mathematical society, 115, 1083-1088, (1992) · Zbl 0756.39005
[9] Kocic, V.L.; Ladas, G.; Rodrigues, I.W., On the rational recursive sequences, Journal of mathematical analysis and applications, 173, 127-157, (1993) · Zbl 0777.39002
[10] Kosmala, W.; Kolenovic, M.R.S.; Ladas, G.; Teixeira, C.T., On the recursive sequence \(y_{n + 1} = \frac{p + y_{n - 1}}{\mathit{qy}_n + y_{n - 1}}\), Journal of mathematical analysis and applications, 251, 571-586, (2000) · Zbl 0967.39004
[11] Kulenovic, M.R.S.; Ladas, G., Dynamics of second order rational difference equations with open problems and conjectures, (2002), Chapman and Hall/CRC Boca Raton · Zbl 0981.39011
[12] Kulenovic, M.R.S.; Ladas, G.; Sizer, W.S., On the recursive sequence \(x_{n + 1} = \frac{\alpha x_n + \beta x_{n - 1}}{\gamma x_n + \mathit{Cx}_{n - 1}}\), Mathematical science and researches hot-line, 2, 5, 1-16, (1998) · Zbl 0960.39502
[13] Kuruklis, S.A.; Ladas, G., Oscillation and global attractivity in a logistic model, Quarterly of applied mathematics, 50, 227-233, (1992) · Zbl 0799.39004
[14] Sedaghat, H., Geometric stability conditions for higher order difference equations, Journal of mathematical analysis and applications, 224, 225-272, (1998) · Zbl 0911.39003
[15] Sedaghat, H., Nonlinear difference equations, theory with applications to social science models, (2003), Kluwer Academic Publishers Dordrect · Zbl 1020.39007
[16] M. Jaberi Douraki, M. Dehghan, M. Razzaghi, On the higher order rational recursive sequence \(x_n = \frac{A}{x_{n - k}} + \frac{B}{x_{n - 3 k}}\), Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2005.04.007. · Zbl 1094.39010
[17] M. Jaberi Douraki, M. Dehghan, M. Razzaghi, The qualitative behavior of solutions of a nonlinear difference equation, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2004.12.017. · Zbl 1128.39005
[18] M. Jaberi Douraki, M. Dehghan, A. Razavi, On the global behavior of higher order recursive sequences, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2004.09.065. · Zbl 1127.39016
[19] M. Jaberi Douraki, The study of some classes of nonlinear difference equations, M.Sc. Thesis, Department of Applied Mathematics, Amirkabir University of Technology, July 2004, Tehran, Iran.
[20] M. Dehghan, M. Jaberi Douraki, Dynamics of a rational difference equation using both theoretical and computational approaches, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2004.09.009. · Zbl 1085.39006
[21] M. Nasri, M. Dehghan, M. Jaberi Douraki, Study of a system of non-linear difference equations arising in a deterministic model for HIV infection, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2005.01.133. · Zbl 1087.92054
[22] M. Dehghan, M. Nasri, M.R. Razvan, Global stability of a deterministic model for HIV infection in vivo, submitted for publication. · Zbl 1142.92336
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