Oscillation of second order half-linear difference equations (II)

In this paper, we obtain some sufficient conditions for the oscillation of all solutions of the second order half-linear difference equation Δ ( r n | Δ x n | α − 2 Δ x n ) + p n | x n + 1 | α − 2 x n + 1 = 0 , n = 0.1 , 2 , … , where Δ x n = x n + 1 − x n is the forward difference operator,  { r n } is a sequence of positive real numbers, { p n } is a sequence of nonnegative real numbers and α > 1 . One open problem in Remark 3 of Rehak (2000) [1] is solved.