Solvability of a system of higher order nonlinear difference equations

Abstract

In this paper we show that the system of difference equations xn = ayn-k + dyn-kxn-(k+l)/bxn-(k+l) + cyn-l, yn = αxn-k + δxn-kyn-(k+l)/βyn-(k+l) + γxn-l, where n ε ℕ0, k and l are positive integers, the parameters a, b, c, d, α, β, γ, δ are real numbers and the initial values x-j, y-j, j = 1, k + l, 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.