Oscillatory properties for Emden–Fowler type difference equations with oscillating coefficients

Abstract

In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form $\Delta W_n+r_n{y}_{n-\tau }^{\beta }=0\text{,}n\ge n_0\text{,}$where $W_n=p_n{\left({\Delta }^3{v}_n\right)}^{\alpha }$ and $v_n=y_n+q_n{y}_{n-\sigma }$. For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.