Oscillation and nonoscillation theorems for fourth order difference equations (Q1430438)

The author studies the following fourth order difference equations of the form \[ \Delta^{4}y_n=f(n,y_n), \quad n\in \mathbb N=\{0,1,2,\dots\},\tag{1} \] where \(\Delta\) is the forward difference operator, \(\Delta y_n=y_{n+1}-y_n\), \(\Delta^{k}y_n=\Delta(\Delta^{k-1}y_n)\) for \(k=2,3,4\), and \(f:\mathbb N\times \mathbb R\to \mathbb R\) satisfies the following condition \[ xf(n,x)<0 \quad \text{for} \quad n\in \mathbb N,\;x\in \mathbb R\backslash \{0\}. \] Some oscillation and nonoscillation theorems of Eq. (1) are established.