Oscillation and nonoscillation criteria for second order quasilinear difference equations

New oscillation and nonoscillation theorems are obtained for the second order quasilinear difference equation Δ(|Δxn−1|ρ−1Δxn−1)+pn|xn|ρ−1xn=0, where ρ>0 is a constant and {pn}n=1∞ is a real sequence with pn⩾0.