Oscillatory properties for Emden-Fowler type difference equations with oscillating coefficients (Q6618270)

This paper deals with a fourth-order difference equation with oscillating coefficients of the form\N\[\N\Delta W_{n}+r_{n}y_{n-\tau }^{\beta }=0,\qquad n\in\mathbb{N},\N\]\Nwhere\N\[\NW_{n}=p_{n}(\Delta ^{3}v_{n})^{\alpha },~v_{n}=y_{n}+q_{n}y_{n-\sigma }.\N\]\NAssuming that \(\alpha \) is a ratio of odd integers, sufficient conditions are obtained for the oscillation of bounded solutions. Then in the case of \(\alpha >\beta\), a condition is given for the oscillation of all solutions. Moreover, two examples are given to illustrate the main results.