Some oscillation criteria for difference equations (Q1591921)

Consider the difference equation \[ x_{n+1}- x_n+p_nx_{n-k}=0, \quad n=0,1,2, \dots\tag{1} \] where \(\{p_n\}\) is a sequence of nonnegative real numbers and \(k\) is a positive integer. New sufficient conditions for the oscillation of all solutions of (1) are established.