Advanced Search

Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form $$\Delta \left(a_n\left(\Delta \left(b_n{\left(\Delta y_n\right)}^{\alpha }\right)\right)\right)+q_{n}f\left(y_{\sigma \left(n\right)}\right)=0$$ to have property $\left(\mathrm{A}\right)$ or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.