The positive periodic solutions to a class of periodic Lotka-Volterra-type systems with infinite delay
type: Item
instance of: scholarly article
zbMATH Open document ID: 0991.34059
publication date: 2002-08-18T00:00:00Z
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1656178
zbMATH Keywords: infinite delay
zbMATH Keywords: Lotka-Volterra-type system
zbMATH Keywords: positive periodic solution
zbMATH Keywords: global asymptotic stability
author: Zhidong Teng
MaRDI profile type: Publication
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title: The positive periodic solutions to a class of periodic Lotka-Volterra-type systems with infinite delay
published in: Acta Mathematica Scientia. Series A. (Chinese Edition)
review text: Here, the existence of positive periodic solutions to the following periodic Lotka-Volterra-type system with delays NEWLINE\[NEWLINE\frac{dx_i(t)}{dt}= x_i(t)(a_i(t)-b_i(t)x_i(t)-f_i(t, x_t)),\quad i= 1,2,\cdots,n,NEWLINE\]NEWLINE is studied, with \(t\in \mathbb{R}\), \(x(t)= (x_1(t), x_2(t), \dots, x_n(t))\in \mathbb{R}^n\), \(x_t\in C^n\) and \(x_t(s)= x(t+s)\). By using Schauder's fixed-point theorem, a general criterion for the existence of positive periodic solutions is obtained, and some main results in the references are improved and extended.
reviewed by: Lansun Chen
description: scientific article; zbMATH DE number 1656178