Solvability of a system of higher order nonlinear difference equations

In this paper we show that the system of difference equations x(n) = ay(n-k) + d(yn)-k(xn)-(k+l)/bx(n)-(k+l) + cy(n-l), y(n) = ax(n)-k + delta x(n)-ky(n)-(k+l)/beta y(n)-(k+l) +gamma x(n-l), where n is an element of N-0, k and l are positive integers, the parameters a, b, c, d, alpha, beta,gamma, delta are real numbers and the initial values x(-j), y(-j), j = (1, k + l$$) over bar, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.