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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 21, Issue 4, 2002, pp. 1015–1025**

**DOI: 10.4171/ZAA/1123**

Published online: 2002-12-31

Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay

Yuji Liu^{[1]}and Weigao Ge

^{[2]}(1) Beijing Institute of Technology, China

(2) Beijing Institute of Technology, China

Consider the non-autonomous logistic model $$\Delta x_n = p_n x_n \frac{1–x_n–k_n}{1+\lambda x_n–k_n}^r \;\;\;(n≥0)$$ where $\Delta x_n = x-{n+1} – x_n$, {$p_n$} is a sequence of positive real numbers, {$k_n$} is a sequence of non-negative integers such that {$n–k_n$} is non-decreasing, $\lambda \in [0,1]$, and $r$ is the ratio of two odd integers. We obtain new sufficient conditions for the attractivity of the equilibrium $x = 1$ of the model and conditions that guarantee the solution to be positive, which improve and generalize some recent results established by Phios and by Zhou and Zhang.

*Keywords: *Global attractivity, difference equations, oscillation

Liu Yuji, Ge Weigao: Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay. *Z. Anal. Anwend.* 21 (2002), 1015-1025. doi: 10.4171/ZAA/1123