Some properties and expressions of solutions for a class of nonlinear difference equation

Abstract

In this paper we study some properties of solutions of difference equation x _n+1 = ax _n-2 +bx _n-2x _n-3/cx _n + dx _n-3, n=0, 1,..., where the initial conditions x _-3, x _-2, x _-1, x _o are arbitrary positive real numbers and a,b,c,d are constants. Also, we give the expressions of solutions for some special cases of this equation.