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On the recursive sequence $x_{n+1} = \max \left\{ c, \frac {x_n^p}{x_{n-1}^p} \right\}$. (English) Zbl 1152.39012
This work studies the boundedness and global attractivity for the posivitive solutions of the difference equation $x_{n+1}= \max\{c,{x^p_n\over x^p_{n-1}}\}$, $n\in\bbfN_0$ with $p,c\in(0,+\infty)$. It is shown that: (a) there exist unbounded solutions whenever $p\ge 4$; (b) all positive solutions are bounded when $p\in(0, 4)$; (c) every positive solution is eventually equal to 1 when $p\in(0, 4)$ and $c\ge 1$; (d) all positive solutions converge to 1 whenever $p,c\in(0,1)$.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
[1] Amleh, A. M.; Hoag, J.; Ladas, G.: A difference equation with eventually periodic solutions. Comput. math. Appl. 36, No. 10--12, 401-404 (1998) · Zbl 0933.39030
[2] Cinar, C.; Stević, S.; Yalçinkaya, I.: On positive solutions of a reciprocal difference equation with minimum. J. appl. Math. comput. 17, No. 1--2, 307-314 (2005) · Zbl 1074.39002
[3] Feuer, J.: On the eventual periodicity of xn+1=max${1xn,Anxn-1}$ with a period-four parameter. J. difference equ. Appl. 12, No. 5, 467-486 (2006)$ · Zbl 1095.39016
[4] Kent, C. M.; Kustesky, M.; Nguyen, A. Q.; Nguyen, B. V.: Eventually periodic solutions of xn+1=max{An/xn,Bn/xn-1} when the parameters are two cycles. Dyn. contin. Discrete impuls. Syst. ser. A math. Anal. 10, No. 1--3, 33-49 (2003)
[5] Kent, C. M.; Radin, M. A.: On the boundedness nature of positive solutions of the difference equation xn+1=max{An/xn,Bn/xn-1} with periodic parameters. Dyn. contin. Discrete impuls. Syst. ser. B appl. Algorithms, No. Suppl., 11-15 (2003)
[6] Ladas, G.: Open problems and conjectures. J. difference equ. Appl. 2, 339-341 (1996)
[7] Mishev, D. P.; Patula, W. T.; Voulov, H. D.: A reciprocal difference equation with maximum. Comput. math. Appl. 43, 1021-1026 (2002) · Zbl 1050.39015
[8] Mishkis, A. D.: On some problems of the theory of differential equations with deviating argument. Uspekhi mat. Nauk 32:2, No. 194, 173-202 (1977)
[9] E.P. Popov, Automatic Regulation and Control, Moscow, 1966 (in Russian)
[10] Stević, S.: On the recursive sequence xn+1=A\prodi=0kxn-i+1\prodj=k+22(k+1)xn-j. Taiwanese J. Math. 7, No. 2, 249-259 (2003)