Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations

Abstract

In this paper, we consider the second-order neutral delay difference equation with positive and negative coefficients

where $c\in \mathbb{R}$, $k\ge 1$ and $m,l\ge 0$ are integers, $\{r_n{\}}_{n=n_0}^{\infty },\{p_n{\}}_{n=n_0}^{\infty }$ and $\{q_n{\}}_{n=n_0}^{\infty }$ are sequences of non-negative real numbers. We obtain global results (with respect to $c$) which are some sufficient conditions for the existences of non-oscillatory solutions.