Oscillation of first order neutral difference equations

Abstract

In this paper, we consider a class of first order neutral difference equations of the form$$\Delta[r(n)(x(n)+p(n) x(n-\tau))]+q(n) x(n-\sigma)=0, \quad n \geq n_0$$Some sufficient conditions for the oscillation of all solutions of given system are established. Our result extend and improve some of the previous results in the literature. Some examples are considered to illustrate our results.