On some periodic systems of max-type difference equations

We show that all positive solutions to the system of max-type difference equations x(n)((1)) = max(1 <= i <= m1) {f(1i)(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 <= m2) {f(2i)(x(n-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) {f(li)(x(n-ki,1(l))((1)), x(n-ki,2(l))((2)), ... , x(n-ki,l(l))((l)), n), x(n-s)((l))}, n is an element of 2 N-0, where s, l, m(j), k(i,t)((t)) is an element of N, j, t is an element of {1, ..., l}, and for a fixed j, i is an element of {1, ..., m(j)}, and where the functions f(ji) : (0, infinity)(l) x N-0 -> (0, infinity), j is an element of {1, ..., l}; i is an element of {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. (C) 2012 Elsevier Inc. All rights reserved.