Abstract
In this paper, we investigate the behavior of solutions of the difference equation
x(n+1) = alpha(x(n-1) + x(n-2)) + (alpha -1)x(n-1)x(n-2)/x(n-1)x(n-2) + alpha, n = 0, 1, 2, ...,
where the initial conditions 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.