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

summary: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 $(\gamma <1)$