Some Oscillation Results for Even Order Delay Difference Equations with a Sublinear Neutral Term

Abstract

In this paper, some new results are obtained for the even order neutral delay difference equation $\mathrm{\Delta }\left(a_n{\mathrm{\Delta }}^{m-\mathrm{1}}\left(x_n+p_n{x}_{n-k}^{\alpha }\right)\right)+q_n{x}_{n-\mathcal{l}}^{\beta }=\mathrm{0}$, where $m\ge \mathrm{2}$ is an even integer, which ensure that all solutions of the studied equation are oscillatory. Our results extend, include, and correct some of the existing results. Examples are provided to illustrate the importance of the main results.