On a higher-order system of difference equations

Abstract

Here we study the following system of difference equations where f and g are increasing real functions such that f(0)= g(0) = 0, and coefficients an, bn, cn, an, αn, βn, γn n ε ℕ0, and initial values x-i, y-i, i ε {1, 2,..., 2k} are real numbers. We show that the system is solvable in closed form, and study asymptotic behavior of its solutions.