Solvability of a (k+l)-order nonlinear difference equation

WOS:000674130800021It is shown that the following (k + l)-order nonlinear difference equation x(n) = x(n-k)x(n-k-l)/x(n-l) (a(n) + b(n)x(n-k)x(n-k-l)), n is an element of N-0, where k, l is an element of N, (a(n))(n is an element of N0), (b(n))(n is an element of N0) and the initial values x(-i), i = (1, K + l) over bar, are real numbers, can be solved and extended some results in literature. Also, by using obtained formulas, we give the forbidden set of the initial values for aforementioned equation and study the asymptotic behavior of well-defined solutions of above difference equation for the case k = 3, l = k