Oscillation criteria of third order nonlinear neutral difference equations

Abstract

In this paper we consider the third order nonlinear neutral difference equation of the form$$\Delta\left(r_n\left(\Delta^2\left(x_n \pm p_n x_{\sigma(n)}\right)\right)^\alpha\right)+f\left(n, x_{\tau(n)}\right)=0,$$we establish some sufficient conditions which ensure that every solution of this equation are either oscillatory or converges to zero. Examples are provided to illustrate the main results.