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

### Yong Zhou

Xiangtan University, Xiangtan, Hunan, China### Y. Q. Huang

Xiangtan University, Hunan, China

## Abstract

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

$\Delta r_n \Delta (x_n + cx_{n–k} + p_{n+1}x_{n+1–l} = 0$

where $c \in \mathbb R, k ≥ 1$ and $m, l ≥ 0$ are integers, $\lbrace r_n\rbrace^\infty _{n=n0}, \lbrace p_n\rbrace ^\infty _{n=n0}$ and $\lbrace q_n \rbrace ^\infty _{n=n0}$ 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.

## Cite this article

Yong Zhou, Y. Q. Huang, Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations. Z. Anal. Anwend. 20 (2001), no. 4, pp. 1065–1074

DOI 10.4171/ZAA/1060