Frequent Oscillation Criteria for a Delay Difference Equation ¹

Chuan-Jun Tian, Sui Sun Cheng, and Sheng-Li Xie

Funkcialaj Ekvacioj, 46 (2003), 421-439

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Abstract:

This paper is concerned with the linear delay difference equation

$$x_{n+1}-x_{n}+p_{n}x_{n-k}=0,\ n=0,1,2,\cdots ,$$

where $k$ is a nonnegative integer and $\{p_{n}\}_{n=0}^{\infty }$ is a real sequence. Sufficient conditions for this equation to be frequently oscillatory are derived.

AMS Subject Classification : 39A10

Key Words: Difference equation, Frequent oscillation.