Oscillation of solutions of neutral difference equations with a nonlinear neutral term *

The oscillatory behavior of solutions of the neutral difference equations with nonlinear neutral term,Δ(xn−pnxn−τα)+qnxn−σβ=0,n≥n0is studied in the case when a ≠ 1. A necessary and sufficient oscillatory conditions for the case 0 < a < 1 and an almost “sharp” oscillatory and nonoscillatory criteria for the case a > 1 are obtained.