Oscillation criteria for even order neutral difference equations

Abstract

In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form $\Delta^m(x_n+ax_{n-\tau_1}+bx_{n+\tau_2})+p_nx_{n-\sigma_1}^{\alpha}+q_nx_{n+\sigma_2}^{\beta}=0,\quad n\geq n_0\gt0,$ where $m\geq 2$ is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.