References
-
A. M. Amleh, E. A. Grove, D. A. Georgiou, On the recursive sequence
$x_{n+1} = \alpha+x_{n-1}/x_{n}$ , J. Math. Anal. Appl., 233(1999), no. 2, 790-798. https://doi.org/10.1006/jmaa.1999.6346 -
K. S. Berenhaut, J. D. Foley, S. Stevie, The global attractivity of the rational difference equation
$y_{n} = 1 + \frac{y_{n-k}}{y_{n-m}}$ , Proc. Amer. Math. Soc., 135(2007), no. 4, 1133-1140. https://doi.org/10.1090/S0002-9939-06-08580-7 -
K. S. Berenhaut, K. M. Donadio, J. D. Foley, On the rational recursive sequence
$y_{n} = A + \frac{y_{n-1}}{y_{n-m}}$ for small A, Appl. Math. Lett., 21(2008), no. 9, 906-909. https://doi.org/10.1016/j.aml.2007.07.033 -
R. DeVault, W. Kosmala, G. Ladas, S. W. Schultz, Global behavior of
$y_{n+1 = \frac{p+y_{n-k}}{qy_{n}+y_{n-k}}}$ , Proceedings of the Third World Congress of Nonlinear Analysts, Part 7 (Catania, 2000). Nonlinear Anal. 47(2001), no. 7, 4743-4751. https://doi.org/10.1016/S0362-546X(01)00586-7 -
H. M. El-Owaidy, A. M. Ahmed, M. S. Mousa, On asymptotic behaviour of the difference equation
$x_{n+1} = \alpha + \frac{x_{n-k}}{x_{n}}$ , Appl. Math. Comput., 147(2004), no. 1, 163-167. https://doi.org/10.1016/S0096-3003(02)00659-8 - E. A. Grove and G. Ladas, Periodicities in nonlinear difference equations, Advances in Discrete Mathematics and Applications, 4. Chapman and Hall/CRC, Boca Raton, FL, 2005.
- D. Mehdi, R. Narges, On the global behavior of a high-order rational difference equation, Comput. Phys. Comm., (2009), In Press, Available online 7 December 2008.
-
S. Ozen, I. Ozturk, F. Bozkurt, On the recursive sequence
$\frac{\alpha+y_{n-1}}{\beta+y_{n}} + \frac{y_{n-1}}{y_{n}}$ , Appl. Math. Comput., 188(2007), no. 1, 180-188. https://doi.org/10.1016/j.amc.2006.09.106 -
M. Saleh, M. Aloqeili, On the rational difference equation
$A + \frac{y_{n-k}}{y_{n}}$ , Appl. Math. Comput., 171(2005), no. 2, 862-869. https://doi.org/10.1016/j.amc.2005.01.094 - S. Stevic, Asymptotic periodicity of a higher-order difference equation, Discrete Dyn. Nat. Soc., 2007, Art. ID 13737, 9 pp.
-
T. Sun, H. Xi, The periodic character of the difference equation
$x_{n+1} = f(x_{n-l+1}, x_{n-2k+1})$ , Adv. Difference Equ., 2008, Art. ID 143723, 6 pages.