JournalszaaVol. 20, No. 4pp. 1065–1074

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

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

ΔrnΔ(xn+cxnk+pn+1xn+1l=0\Delta r_n \Delta (x_n + cx_{n–k} + p_{n+1}x_{n+1–l} = 0

where cR,k1c \in \mathbb R, k ≥ 1 and m,l0m, l ≥ 0 are integers, {rn}n=n0,{pn}n=n0\lbrace r_n\rbrace^\infty _{n=n0}, \lbrace p_n\rbrace ^\infty _{n=n0} and {qn}n=n0\lbrace q_n \rbrace ^\infty _{n=n0} are sequences of non-negative real numbers. We obtain global results (with respect to cc) 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