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Consider the delay difference equation
where {pn } is a sequence of nonnegative real numbers and k is a positive integer. We obtain respectively sufficient conditions for all solutions of Eq. (1) to oscillate and the existcnce of a nonoscillatory solution of Eq. (1). Our results improve the known results in [1,3] and also solve an open problem in [4]. The oscillation of a discrete delay logistic equation is also studied.
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