New oscillation criteria for nonlinear higher order neutral difference equation (Q1959066)

The author considers the oscillatory behaviour of higher-order difference equations of the form \[ \Delta^m[x_n- p_nx_{n-\tau}]+ \sum^t_{i=1} Q_i(n) f(x_{n-\sigma_i}), \] where \(\Delta\) is the forward difference operator defined by \(\Delta x_n= x_{n+1}- x_n\) and for \(i> 1\), \(\Delta^i\) is the \(i\)th order forward difference operator \(\Delta^i x_n= \Delta(\Delta^{i-1} x_n)\). \(\tau\) and \(\sigma_i\), \(1\leq i\leq r\) are fixed nonnegative integers, \(\{p_n\}\) is a real sequence and \(\{Q_i(n)\}^r_{i=1}\) is a nonnegative real sequence.