Abstract:
It is shown that the following (k + l)-order nonlinear difference equation
xn =
xn−kxn−k−l
xn−l (an + bnxn−kxn−k−l)
, n ∈ N0,
where k, l ∈ N, (an)n∈N0
, (bn)n∈N0
and the initial values x−i, i = 1, k + l, 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.
