Oscillation of linear difference equations with deviating arguments (Q1600394)

The difference equation with deviating arguments \[ \Delta^2 u(k)+ \sum^m_{j=1} p_j(k) u(\sigma_j(k))= 0, \] is considered, where \(\Delta u(k)= u(k+1)- u(k)\), \(\Delta^2= \Delta\circ \Delta\), \(p_j\geq 0\), and \(\lim_{k\to\infty} \sigma_j(k)= \infty\), \(j= 1,\dots, m\). Sufficient conditions are obtained for all proper solutions of the equation to be oscillatory.