Solvability of a system of nonlinear difference equations of higher order

Abstract

In this paper, we show that the following higher-order system of nonlinear difference equations, xn=xn-kyn-k-l/yn-l(an+bnxn-kyn-k-l, yn=yn-kxn-k-l/xn-l(?n+ßnyn-kxn-k-l), n?0, where k, l,? , (an)n ? 0, (bn)n ? 0, (?n)n ? 0, (ßn)n ? 0 and the initial values x-i; y-i, i = 1, k + l , are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case k = 2, l = k. © Tübitak.