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Let a, c [euro] (0, ∞), b [euro] [IML0001] and let k be a nonnegative integer. We obtain necessary and sufficient conditions for all positive solutions of the nonlinear difference equation [IML0002] to oscillate about its positive equilibrium. When k = 0, we obtain necessary and sufficient conditions for the positive equilibrium of Eq. (∗) to be a global attractor of all positive solutions.
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