zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On some periodic systems of max-type difference equations. (English) Zbl 1280.39012

Summary: We show that all positive solutions to the system of max-type difference equations

x n (1) =max 1im 1 f 1i x n-k i,1 (1) (1) ,x n-k i,2 (1) (2) ,,x n-k i,l (1) (l) ,n,x n-s (1) ,
x n (2) =max 1im 2 f 2i x n-k i,1 (2) (1) ,x n-k i,2 (2) (2) ,,x n-k i,l (2) (l) ,n,x n-s (2) ,
x n (l) =max 1im l f li x n-k i,1 (l) (1) ,x n-k i,2 (l) (2) ,,x n-k i,l (l) (l) ,n,x n-s (l) ,

n 0 , where s,l,m j ,k i,t (j) , t{1,,l}, and for a fixed j,i{1,,m j }, and where the functions f ji :(0,) l × 0 (0,), j{1,,l}, i{1,,m j } satisfy some conditions, are eventually periodic with (not necessarily prime) period s. A related result for the corresponding system of min-type difference equations is also proved.

MSC:
39A23Periodic solutions (difference equations)
39A22Growth, boundedness, comparison of solutions (difference equations)
39A10Additive difference equations
References:
[1]Berenhaut, K.; Foley, J.; Stević, S.: Boundedness character of positive solutions of a MAX difference equation, J. differ. Equat. appl. 12, No. 12, 1193-1199 (2006) · Zbl 1116.39001 · doi:10.1080/10236190600949766
[2]Berg, L.; Stević, S.: Periodicity of some classes of holomorphic difference equations, J. differ. Equat. appl. 12, No. 8, 827-835 (2006) · Zbl 1103.39004 · doi:10.1080/10236190600761575
[3]Elsayed, E. M.; Iričanin, B.: On a MAX-type and a MIN-type difference equation, Appl. math. Comput. 215, No. 2, 608-614 (2009) · Zbl 1178.39010 · doi:10.1016/j.amc.2009.05.045
[4]Elsayed, E. M.; Iričanin, B.; Stević, S.: On the MAX-type equation xn+1=maxAn/xn,xn-1, Ars. combin. 95, 187-192 (2010)
[5]Elsayed, E. M.; Stević, S.: On the MAX-type equation xn+1=maxA/xn,xn-2, Nonlinear anal. TMA 71, 910-922 (2009)
[6]Feuer, J.: On the eventual periodicity of xn+1=max1/xn,An/xn-1 with a period-four parameter, J. differ. Equat. appl. 12, No. 5, 467-486 (2006) · Zbl 1095.39016 · doi:10.1080/10236190600574002
[7]Grove, E. A.; Ladas, G.: Periodicities in nonlinear difference equations, (2005)
[8]Iričanin, B.; Stević, S.: Eventually constant solutions of a rational difference equation, Appl. math. Comput. 215, 854-856 (2009) · Zbl 1178.39012 · doi:10.1016/j.amc.2009.05.044
[9]Kent, C. M.; Kustesky, M.; Nguyen, M. A. Q.; Nguyen, B. V.: Eventually periodic solutions of xn+1=maxAn/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) · Zbl 1038.39006
[10]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. Algor., No. 11 – 15 (2003)
[11]Mishev, D. P.; Patula, W. T.; Voulov, H. D.: Periodic coefficients in a reciprocal difference equation with maximum, Panamer. math. J. 13, No. 3, 43-57 (2003) · Zbl 1050.39016
[12]Papaschinopoulos, G.; Schinas, C.; Hatzifilippidis, V.: Global behavior of the solutions of a MAX-equation and of a system of two MAX-equations, J. comput. Anal. appl. 5, No. 2, 237-254 (2003) · Zbl 1034.39008 · doi:10.1023/A:1022833112788
[13]Stefanidou, G.; Papaschinopoulos, G.; Schinas, C.: On a system of MAX difference equations, Dynam. contin. Discrete impuls. Syst. ser. A 14, No. 6, 885-903 (2007) · Zbl 1142.39012
[14]Stević, S.: Global stability and asymptotics of some classes of rational difference equations, J. math. Anal. appl. 316, 60-68 (2006) · Zbl 1090.39009 · doi:10.1016/j.jmaa.2005.04.077
[15]Stević, S.: Existence of nontrivial solutions of a rational difference equation, Appl. math. Lett. 20, 28-31 (2007) · Zbl 1131.39009 · doi:10.1016/j.aml.2006.03.002
[16]Stević, S.: On the recursive sequence xn+1=maxc,xnp/xn-1p, Appl. math. Lett. 21, No. 8, 791-796 (2008)
[17]Stević, S.: Boundedness character of a class of difference equations, Nonlinear anal. TMA 70, 839-848 (2009) · Zbl 1162.39011 · doi:10.1016/j.na.2008.01.014
[18]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
[19]Stević, S.: On a generalized MAX-type difference equation from automatic control theory, Nonlinear anal. TMA 72, 1841-1849 (2010) · Zbl 1194.39007 · doi:10.1016/j.na.2009.09.025
[20]Stević, S.: On a nonlinear generalized MAX-type difference equation, J. math. Anal. appl. 376, 317-328 (2011) · Zbl 1208.39014 · doi:10.1016/j.jmaa.2010.11.041
[21]Stević, S.: On a system of difference equations, Appl. math. Comput. 218, 3372-3378 (2011)
[22]Stević, S.: On a system of difference equations with period two coefficients, Appl. math. Comput. 218, 4317-4324 (2011)
[23]Stević, S.: On the difference equation xn=xn-2/(bn+cnxn-1xn-2), Appl. math. Comput. 218, 4507-4513 (2011)
[24]Stević, S.: Periodicity of a class of nonautonomous MAX-type difference equations, Appl. math. Comput. 217, 9562-9566 (2011) · Zbl 1225.39018 · doi:10.1016/j.amc.2011.04.022
[25]Stević, S.: On a third-order system of difference equations, Appl. math. Comput. 218, 7649-7654 (2012)
[26]Stević, S.: On some solvable systems of difference equations, Appl. math. Comput. 218, 5010-5018 (2012)
[27]Stević, S.: On the difference equation xn=xn-k/(b+cxn-1·xn-k), Appl. math. Comput. 218, 6291-6296 (2012)
[28]Sun, T.; Bin, Q.; Xi, H.; Han, C.: Global behavior of difference equation xn+1=max1/xn,An/xn-1, Abstr. appl. Anal. 2009 (2009) · Zbl 1167.39303 · doi:10.1155/2009/152964
[29]Voulov, H. D.: On the periodic nature of the solutions of the reciprocal difference equation with maximum, J. math. Anal. appl. 296, No. 1, 32-43 (2004) · Zbl 1053.39023 · doi:10.1016/j.jmaa.2004.02.054
[30]Voulov, H. D.: On a difference equation with periodic coefficients, J. differ. Equat. appl. 13, No. 5, 443-452 (2007) · Zbl 1121.39011 · doi:10.1080/10236190701264651
[31]Yang, X.; Liao, X.: On a difference equation with maximum, Appl. math. Comput. 181, 1-5 (2006) · Zbl 1148.39303 · doi:10.1016/j.amc.2006.01.005