Abstract
In this paper, we investigate the behavior of solutions of the difference equation
x(n+1) = alpha(x(n-2) + x(n-3))-(alpha-1)x(n-2)x(n-3)/x(n-2)x(n-3)-alpha , n = 0,1,2, ...,
where the initial conditions x(-3),x(-2),x(-1),x(0) are arbitrary non-negative real numbers and the parameter alpha is an element of [1,infinity). More precisely, we study the boundedness, stability, and oscillation of the solutions of this equation.