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Sufficient conditions are obtained so that every solution of , τ > 0 and σ ≥ 0, oscillates or tends to zero as t → ∞. Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞. The technique employed in this paper is motivated by Lemma 2.1 (see Section 2). The results hold true for homogeneous equations associateddoi:10.4064/ap81-2-1 fatcat:lzvntezv5fgmziisfsbk6gneje