Oscillation and non-oscillation for second-order linear difference equations

We prove new oscillation and non-oscillation theorems for the second-order linear difference equation Δ2xn−1 + pnxn = 0, where {pn}n=1∞ is a real sequence with pn ⩾ 0. These results are extensions of earlier results of Zhang and Zhou [Comput. Math. Appl. 39 (2000) 1-7].