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Qualitative properties of some higher order difference equations. (English) Zbl 1189.39014
Summary: We present sufficient conditions which guarantee that all positive solutions of some higher order rational difference equations are global asymptotically stable. The boundedness of the solutions and the existence of prime period two solutions of such equations are also investigated.
39A22Growth, boundedness, comparison of solutions (difference equations)
39A23Periodic solutions (difference equations)
39A30Stability theory (difference equations)
[1]Saaty, T. L.: Modern nonlinear equations, (1967) · Zbl 0148.28202
[2]Leech, J.: The rational cuboid revisited, Amer. math. Monthly 84, 518-533 (1977) · Zbl 0373.10011 · doi:10.2307/2320014
[3]Conway, J. H.; Coxeter, H. S. M.: Triangulated polygons and frieze patterns, Math. gaz. 57, No. 400, 87-94 (1973) · Zbl 0285.05028 · doi:10.2307/3615344
[4]Kocic, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications, (1993)
[5]Kulenovic, M. R. S.; Ladas, G.: Dynamics of second order rational difference equations, (2001)
[6]Elabbasy, E. M.; El-Metwally, H.; Elsayed, E. M.: Global attractivity and periodic character of a fractional difference equation of order three, Yokohama math. J. 53, 91-102 (2007) · Zbl 1138.39006
[7]El-Metwally, H.; Grove, E. A.; Ladas, G.; Voulov, H. D.: On the global attractivity and the periodic character of some difference equations, J. difference equ. Appl. 7, 837-850 (2001) · Zbl 0993.39008 · doi:10.1080/10236190108808306
[8]El-Morshedy, Hassan A.: New explicit global asymptotic stability criteria for higher order difference equations, J. math. Anal. appl. 336, No. 1, 262-276 (2007) · Zbl 1186.39022 · doi:10.1016/j.jmaa.2006.12.049
[9]Grove, E. A.; Ladas, G.; Mcgrath, L. C.; El-Metwally, H.: On the difference equation yn+1=yn-(2k+1)+pyn-(2k+1)+qyn-2l, , 433-453 (2004)
[10]Li, Wan-Tong; Fan, Xian-Ling; Zhong, Cheng-Kui: Unbounded positive solutions of higher-order difference equations with singular nonlinear term, Comput. math. Appl. 39, No. 3–4, 177-184 (2000) · Zbl 0959.39005 · doi:10.1016/S0898-1221(99)00343-0
[11]Liz, Eduardo: On explicit conditions for the asymptotic stability of linear higher order difference equations, J. math. Anal. appl. 303, No. 2, 492-498 (2005) · Zbl 1068.39017 · doi:10.1016/j.jmaa.2004.08.048
[12]Kulenovic, M. R. S.; Ladas, G.; Sizer, W. S.: On the recursive sequence xn+1=αxn+βxn-1γxn+δxn-1, Math. sci. Res. hot-line 2, No. 5, 1-16 (1998) · Zbl 0960.39502