Tbilisi Mathematical Journal

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

M. Kara, Y. Yazlik

It is shown that the following (k+l)-order nonlinear difference equation
x_n = x_n-k x_n-k-l / x_n-1(a_n+b_nx_n-kx_n-k-l), n∈N₀,
where k,l∈N, (a_n)_n∈N₀, (b_n)_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.


Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 271-297