Boundedness of a Max-type Fourth Order Difference Equation with Periodic Coefficients
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W. J. Briden, E. A. Grove, G. Ladas and L. C. McGrath, On the nonautonomous equation xn+1 = maxfAn xn ; Bn xn1 g, Proceedings of the Third International Conference on Dierence Equations and Applications, September 1-5, 1997, Taipei Taiwan, Gordon and Breach Science Publishers, 1999, 49-73.
W. J. Briden, E. A. Grove, C. M. Kent and G. Ladas, Eventually periodic solutions of xn+1 = maxf 1 xn ; An xn1 g, Communications on Applied Nonlinear Analisys, 1999, 6(4): 31- 43.
E. A. Grove, C. M. Kent, G. Ladas and M. A. Radin, On xn+1 = maxf 1 xn ; An xn1 g with a period 3 parameter. Fields Institute Communications, 2001, 29: 161-180.
C. M. Kent, M. A. Radin, On the bounddness nature of the positive solutions of the dierence equation xn+1 = maxf 1 xn ; An xn1
g with periodic parameters. Watam Press, 2001, 29: 11-15.
C. P. Kerbert, M. A. Radin, Unbounded solutions of the max-type dierence equation xn+1 =maxfAnxn
; Bnxn2g, Central Europen Journal of Mathematics, 2008, 6(2): 307-324.
A. M. Amleh, J. Hoag and G. Ladas, A dierence equation with eventually periodic solutions,
Computers and Mathematics with Applications, 1998, 36: 401-404.
D. P. Mishev, W. T. Patula and H. D. Voulov, A reciprocal dierence equation with maximum, Computers and Mathematics with Applications, 2002, 43(8-9): 1021-1026.
E. M. Elabbasyd, H. EL-Metwally and E. M. Elsayed, On the periodic nature of some max-type dierence equations, International Journal of Mathematics and Mathematical Sciences, 2005, 14: 2227-2239.
A. Gelisken, C. Cinar, On the global attractivity of a max-type dierence equation, Discrete Dynamics in Nature and Society, 2009, Article ID 812674, 5 pages.
A. Gelisken, C. Cinar and I. Yalcinkaya, On the periodicity of a dierence equation with maximum, Discrete Dynamics in Nature and Society, 2008, Article ID 820629, 11 pages.
X. Li, D. Zhu, G. Xiao , Behavior of solutions of certain recursions involving the maximum, Journal of Mathematics, 2003, 23(2): 199-206.
T. Sun, H. Xi, C. Han and B. Qin, Dynamics of the max-type dierence equation xn = maxf 1 xnm ; An xnrg, Journal of Applied Mathematics and Computing, 2012, 38:173-180.
B. D. Iricanin, E. M. Elsayed, On the max-type dierence equation xn+1 = maxf Axn; xn3g,Discrete Dynamics in Nature and Society, 2010, Article ID 675413, 13 pages.
E. M. Elsayed, B. D. Iricanin, On a max-type and a min-type dierence equation, Applied Mathematics and Computation, 2009, 215: 608-614.
F. Sun, On the asymptotic behavior of a dierence equation with maximum, Discrete Dynamics in Nature and Society, 2008, Article ID 243291, 6 pages.
B. D. Iricanin, The boundedness character of two Stevic-type fourth-order dierence equations, Applied Mathematics and Computation, 2010, 217: 1857-1862.
G. Stefanidou, G. Papaschinopoulos, The periodic nature of the positive solutions of a non-linear fuzzy max-dierence equation, Information Sciences, 2006, 176: 3694-3710.
A. Gelisken, C. Cinar and A. S. Kurbanli, On the asymptotic behavior and periodic nature of a dierence equation with maximum, Computers and Mathematics with Applications, 2010, 59: 898-902.
I. Yalcinkaya, C. Cinar, and A. Gelisken, On the recursive sequence xn+1 = maxfxn;Agx2 nxn1,Discrete Dynamics in Nature and Society, 2010, Article ID 583230, 13 pages.
A. Gelisken, C. Cinar and I. Yalcinkaya, On a max-type dierence equation, Advances in Dierence Equations, 2010, Article ID 584890, 6 pages.
T. Sun, B. Qin, H. Xi and C. Han, Global behavior of the max-type dierence equation , Abstract and Applied Analysis xn+1 = maxf 1 xn
; An xn1 g, 2009, Article ID 152964, 10 pages.
X. Yang, X. Liao and C. Li, On a dierence equation with maximum, Applied Mathematics and Computation, 2006, 181:1-5.
F. Deng, X. Li, Dichotomy of a perturbed Lyness dierence equation, Applied Mathematics and Computation, 2014, 236, 229-234.
E.P. Popov, Automatic Regulation and Control, (in Russian), Moscow, 1966.
A.D. Mishkis, On some problems of the theory of dierential equations with deviating argument, I/MN, 32:2, 1977, 194: 173-202.
DOI: http://dx.doi.org/10.26713%2Fjims.v6i1.240
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