Oscillatory and asymptotic behavior of certain fourth order difference equations (Q1081763)

From authors' introduction: This note is concerned with the solutions of the fourth order linear difference equation \[ \Delta (\Delta^ 3u_ n+p_ nu_{n+2})+p_ n\Delta u_{n+1}+q_ nu_{n+2}=0 \] where \(\Delta\) denotes the differencing operator, i.e. \(\Delta x_ n=x_{n+1}-x_ n\). While no sign conditions are explicitly stated for the real sequences \(\{p_ n\}\), it will be assumed that \(q_ n>0\) for each n.