On the oscillation of certain difference equations

summary:In this paper we study the oscillation of the difference equations of the form \Delta^2x_n+p_n\Delta x_n+f(n, x_{n-g}, \Delta x_{n-h})=0, in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation \Delta^2x_n+p_n\Delta x_n+q_n|x_{n-g}|^{\lambda}|\Delta x_{n-h}|^{\mu}\sgn x_{n-g}=0, where $\lambda$ and $\mu$ are real constants, $\lambda>0$ and $\mu\geq0$