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On a nonlinear generalized max-type difference equation. (English) Zbl 1208.39014
For the difference equation x n =max{A,x n-1 p /x n-k r } with nonnegative entries there are considered 5 cases in which all solutions are bounded, and 2 cases where unbounded solutions exist.
MSC:
39A20Generalized difference equations
39A10Additive difference equations
References:
[1]Berenhaut, K.; Foley, J.; Stević, S.: Boundedness character of positive solutions of a MAX difference equation, J. difference equ. Appl. 12, No. 12, 1193-1199 (2006) · Zbl 1116.39001 · doi:10.1080/10236190600949766
[2]Berezansky, L.; Braverman, E.; Liz, E.: Sufficient conditions for the global stability of nonautonomous higher order difference equations, J. difference equ. Appl. 11, No. 9, 785-798 (2005) · Zbl 1078.39005 · doi:10.1080/10236190500141050
[3]Berg, L.: On the asymptotics of nonlinear difference equations, Z. anal. Anwend. 21, No. 4, 1061-1074 (2002) · Zbl 1030.39006
[4]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 · doi:10.1007/BF02936057
[5]Devault, R.; Kent, C.; Kosmala, W.: On the recursive sequence xn+1=p+(xn-k/xn), J. difference equ. Appl. 9, No. 8, 721-730 (2003) · Zbl 1049.39026 · doi:10.1080/1023619021000042162
[6]Elsayed, E. M.; Iričanin, B.; Stević, S.: On the MAX-type equation xn+1=maxAn/xn,xn-1, Ars combin. 95, 187-192 (2010)
[7]Feuer, J.: On the behaviour of solutions of xn+1=p+(xn-1/xn), Appl. anal. 83, No. 6, 599-606 (2004) · Zbl 1053.39009 · doi:10.1080/00036810410001657260
[8]Feuer, J.: On the eventual periodicity of xn+1=max1/xn,An/xn-1 with a period-four parameter, J. difference equ. Appl. 12, No. 5, 467-486 (2006) · Zbl 1095.39016 · doi:10.1080/10236190600574002
[9]Grove, E. A.; Ladas, G.: Periodicities in nonlinear difference equations, (2005)
[10]Iričanin, B.: A global convergence result for a higher-order difference equation, Discrete dyn. Nat. soc. 2007 (2007)
[11]Karakostas, G. L.: Asymptotic 2-periodic difference equations with diagonally self-invertible responces, J. difference equ. Appl. 6, 329-335 (2000) · Zbl 0963.39020 · doi:10.1080/10236190008808232
[12]Kocić, V. L.; Ladas, G.: Global behaviour of nonlinear difference equations of higher order with applications, (1993)
[13]Kent, C. M.; Radin, M. A.: On the boundedness nature of positive solutions of the difference equation xn+1=maxAn/xn,Bn/xn-1, with periodic parameters, Dyn. contin. Discrete impuls. Syst. ser. B appl. Algorithms (Suppl.), 11-15 (2003)
[14]Mishev, D.; Patula, W. T.; Voulov, H. D.: A reciprocal difference equation with maximum, Comput. math. Appl. 43, 1021-1026 (2002) · Zbl 1050.39015 · doi:10.1016/S0898-1221(02)80010-4
[15]Patula, W. T.; Voulov, H. D.: On a MAX type recurrence relation with periodic coefficients, J. difference equ. Appl. 10, No. 3, 329-338 (2004) · Zbl 1050.39017 · doi:10.1080/10236190310001659741
[16]Pielou, E. C.: Population and community ecology, (1974)
[17]Popov, E. P.: Automatic regulation and control, (1966)
[18]Stević, S.: Behaviour of the positive solutions of the generalized beddington-Holt equation, Panamer. math. J. 10, No. 4, 77-85 (2000) · Zbl 1039.39005
[19]Stević, S.: On the recursive sequence xn+1=A/i=0kxn-i+1/j=k+22(k+1)xn-j, Taiwanese J. Math. 7, No. 2, 249-259 (2003)
[20]Stević, S.: On the recursive sequence xn+1=αn+(xn-1/xn) II, Dyn. contin. Discrete impuls. Syst. 10a, No. 6, 911-917 (2003)
[21]Stević, S.: On the recursive sequence xn+1=α+(xn-1p/xnp), J. appl. Math. comput. 18, No. 1-2, 229-234 (2005) · Zbl 1078.39013 · doi:10.1007/BF02936567
[22]Stević, S.: On the recursive sequence xn+1=A+(xnp/xn-1r), Discrete dyn. Nat. soc. 2007 (2007)
[23]Stević, S.: On the difference equation xn+1=α+(xn-1/xn), Comput. math. Appl. 56, No. 5, 1159-1171 (2008) · Zbl 1155.39305 · doi:10.1016/j.camwa.2008.02.017
[24]Stević, S.: On the recursive sequence xn+1=maxc,xnp/xn-1p, Appl. math. Lett. 21, No. 8, 791-796 (2008)
[25]Stević, S.: Boundedness character of two classes of third-order difference equations, J. difference equ. Appl. 15, No. 11-12, 1193-1209 (2009) · Zbl 1182.39012 · doi:10.1080/10236190903022774
[26]Stević, S.: Global stability of a difference equation with maximum, Appl. math. Comput. 210, 525-529 (2009) · Zbl 1167.39007 · doi:10.1016/j.amc.2009.01.050
[27]Stević, S.: Global stability of a MAX-type equation, Appl. math. Comput. 216, 354-356 (2010) · Zbl 1193.39009 · doi:10.1016/j.amc.2010.01.020
[28]Stević, S.; Iričanin, B.: On a MAX-type difference inequality and its applications, Discrete dyn. Nat. soc. 2010 (2010) · Zbl 1192.39008 · doi:10.1155/2010/975740
[29]Voulov, H. D.: On a difference equation with periodic coefficients, J. difference equ. Appl. 13, No. 5, 443-452 (2007) · Zbl 1121.39011 · doi:10.1080/10236190701264651
[30]Yalçinkaya, I.; Iričanin, B. D.; Çinar, C.: On a MAX-type difference equation, Discrete dyn. Nat. soc. 2007 (2007) · Zbl 1152.39016 · doi:10.1155/2007/47264