Oscillation and Nonoscillation Theorems for a Class of Fourth Order Quasilinear Difference Equations

Abstract

In this paper, we consider certain quasilinear  difference equations$$(A)~~~~~~~~~~~~~~~\Delta^{2}(\mid\Delta^{2}y_{n}\mid^{\alpha-1}\Delta^{2}y_{n})+q_{n}\midy_{\tau(n)}\mid^{\beta-1}y_{\tau(n)}=0$$where \\(a) $\alpha,\beta $ are positive constants;  \\(b) $\{q_{n}\}_{n_{0}}^{\infty}$ arepositive real sequences. $n_{0}\in N_{0}=\{1,2,\cdots \}$.Oscillation and nonoscillation theorems  of the above equation is obtained.