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

### Yuji Liu

Beijing Institute of Technology, China### Weigao Ge

Beijing Institute of Technology, China

## Abstract

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.

## Cite this article

Yuji Liu, Weigao Ge, Existence and Asymptotic Behavior of Positive Solutions of a Non-Autonomous Food-Limited Model with Unbounded Delay. Z. Anal. Anwend. 21 (2002), no. 4, pp. 1015–1025

DOI 10.4171/ZAA/1123