Oscillation of second-order linear difference equations

Abstract In this paper we give new oscillation and nonoscillation criteria for the self-adjoint difference equation Δ(cn−1Δxn−1) + anxn = 0 in terms of the sequence q n =c n / b n b n+1 where bn = cn + cn−1 − an. A necessary and sufficient condition for oscillation is given in the case of qn periodic with period 2.