Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma <1)$.