Abstract
Here we study the following system of difference equations
x(n) = f(-1) (c(n)f(x(n-2k)/a(n) + b(n) Pi(k)(i=1) g(y(n-(2i-1)))f(x(n-2i))),
y(n) = g(-1) (gamma(n)g(y(n-2k))/alpha(n) + beta(n) Pi(k)(i=1) f(x(n-(2i-1)))g(y(n-2i))),
n is an element of N-0, where f and g are increasing real functions such that f(0) = g(0) = 0, and coefficients a(n), b(n), c(n), alpha(n), beta(n), gamma(n), n is an element of N-0, and initial values x-i, y-i, i is an element of {1,2,...,2k} are real numbers. We show that the systems is solvable in closed form, and study asymptotic behavior of its solutions.