In this paper sufficient conditions are obtained for every solution of (*) ((t)y(t-τ))~(n) + Q(t)G(y(t-σ)) = f(t), t ≥ 0, to oscillate or tend to zero as t→∞, for both n odd or even. Here 0 ≤ p(t) ≤ p or -p ≤ p(t) ≤ 0, where p is a positive scalar. The results of this paper hold for linear, super linear or sublinear equations, and answer an open problem suggested by Ladas and Gyori in [1]. The results of the paper are also true for the homogeneous equation associated with (*), and generalize/improve some known results.
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