On the global attractivity and oscillations in a class of second order difference equations f

New global attractivity criteria are obtained for the second order difference nequation [ x_{n+1}=cx_{n}+f(x_{n}-x_{n-1}), quad n=1, 2, ... ] via a nLyapunov-like method. Some of these results are sharp and support recent nrelated conjectures. Also, a necessary and sufficient condition for the noscillation of this equation is obt..