Oscillation Criteria of Second Order Difference Equation With Negative Nonlinear Neutral Term

Abstract

In this paper, the authors obtain sufficient conditions for the oscillatory behavior of neutral delay difference equation of the form \begin{equation*} \Delta(a_n\Delta(x_n-p_nx_{n-k}^{\alpha}))+q_nx_{n-l}^{\beta}=0 \end{equation*} where $\{a_n\},\;\{p_n\}$ and $\{q_n\}$ are positive real sequences, $\alpha$ and $\beta$ are ratios of odd positive integers. Examples are provided to illustrate the main results.