Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On some periodic systems of max-type difference equations
Journal: Applied Mathematics and Computation
Volume: 218
Issue: 23
First page: 11483
Last page: 11487
Issue Date: 1-Aug-2012
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2012.04.077
Abstract: 
We show that all positive solutions to the system of max-type difference equations x n(1)=max 1≤i≤m1{f1i(x n-ki,1(1)(1),x n-ki,2(1)(2),⋯, x n-ki,l(1)(l),n,x n-s(1),x n(2)=max 1≤i≤ m2f2i xn-ki,1(2)(1),x n-ki,2(2)(2), ⋯,x n-ki,l(2)(l),n,x n-s(2),⋮x n(l)=max 1≤i≤ ml{fli(x n-ki,1(l)(1),x n-ki,2(l)(2),⋯,x n-ki,l(l)(l),n),x n-s(l)},n∈ℕ 0, where s,l, mj,k i,t(j)∈ℕ, j,t∈{1,⋯,l}, and for a fixed j, i∈{1,⋯,m j}, and where the functions f ji:(0,∞) l×ℕ 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.
Keywords: Eventually periodic solution | System of max-type difference equations | System of min-type difference equations
Publisher: Elsevier

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