On the Oscillation of Solutions of First-Order Difference Equations with Delay

Abstract

Consider the first order delay difference equation $$\Delta x_{n} + p_{n} x_{\sigma(n)} = 0, \quad n \in {\mathbb N}_0,$$ where $\{p_{n}\}_{n \in {\mathbb N}_0}$ is a sequence of nonnegative real numbers, and $\{\sigma(n)\}_{n \in {\mathbb N}_0}$ is a sequence of integers such that $\sigma(n) \le n-1$, and $\displaystyle \lim_{n \to \infty}\sigma(n) = +\infty$. We obtain similar oscillation criteria of delay differential equations. This criterion is used by more simple method until now.