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.  2004 Elsevier Inc. All rights reserved.