Non-oscillation criterion for Euler type half-linear difference equations with consequences in linear case

We study the oscillation of Euler type half-linear difference equations with asymptotically periodic and bounded coefficients. Applying the adapted Riccati technique, we prove a non-oscillation criterion for the treated equations. Since the obtained criterion is new in several cases, we formulate many consequences explicitly. In particular, the criterion is new for intensively studied linear equations (e.g., with periodic coefficients).