On the solvable nonlinear difference equation of sixth-order

Abstract

In this paper, we deal with the next difference equation   4 5 6 0 1 2 3 4 5 6 , , n n n n n n n n n n x x x x n x x a bx x x x             where a b,  and the initial conditions x i i , 1,2, ,6 ,   are real numbers. Also, we give the form of well-defined solution of aforementioned difference equation. Finally, we study the asymptotic behavior of well-defined solution of this equation by using obtained formulas.