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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 4, 2001, pp. 1065–1074
DOI: 10.4171/ZAA/1060

Published online: 2001-12-31

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

Yong Zhou[1] and Y. Q. Huang[2]

(1) Xiangtan University, Xiangtan, Hunan, China
(2) Xiangtan University, Hunan, China

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.

Keywords: Neutral difference equations, non-oscillatory solutions, existence of solutions

Zhou Yong, Huang Y.: Existence of Non-Oscillatory Solutions of Second-Order Neutral Delay Difference Equations. Z. Anal. Anwend. 20 (2001), 1065-1074. doi: 10.4171/ZAA/1060