Oscillation of second-order half-linear difference equations

Abstract Some new oscillation criteria are obtained for the second-order half-linear difference equation (−1) m+1 δ m y i (n) + σ j=1 N q ij y i (n−T ji )=0, m ⩾1, i=1,…N where α 0 is a ratio of odd positive integers. The method uses techniques based on a Riccati type difference inequality. Examples are inserted to illustrate the results.