Oscillation in a Variable Delay Logistic Difference Equation

摘要

Consider the nonautonomous delay logistic equation △yn = pnyn(1- ynk-ln), n ≥ 0, (1)where {pn}n≥0 is a sequence of nonnegative real numbers, {ln}n≥0 is a sequence of positive integers satisfying lim n→∞(n - ln) = ∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of (1) to oscillate about k which contains the corresponding result in [2] when i = 1.