Oscillation of neutral difference equations with ``maxima'' (Q2772887)

The author presents sufficient condition for oscillation of all the solutions of a difference equation with maxima NEWLINE\[NEWLINE\Delta [x_n+p_nx_{n-k}]+q_n\max_{[n-l,n]}x_s=0\qquad n\in \{n_0,n_0+1,\dots\}\tag{1}NEWLINE\]NEWLINE where \(\Delta x_n=x_{n+1}-x_n\), \([n-l,n]=\{ n-l,n-l+1,\dots,n\}\) and \(k,l\) are positive integers. A nontrivial solution \(\{ x_n \}\) of (1) is said to be nonoscillatory if the terms \(x_n\) are either eventually positive or eventually negative; otherwise, the solution is said to be oscillatory.