Positive periodic solution for a neutral delay competitive system
type: Item
instance of: scholarly article
title: Positive periodic solution for a neutral delay competitive system
zbMATH Open document ID: 1057.34095
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The author considers the neutral delay multispecies ecological competitive system \[ \dot N_i(t)= N_i(t) \left[ r_i(t)- \sum_{j=1}^n a_{ij}(t) N_j(t)- \sum_{j=1}^n b_{ij}(t) N_j(t-\tau_{ij}(t))- \sum_{j=1}^n c_{ij} \dot N_j (t-\sigma_{ij}) \right], \tag{1} \] with initial conditions \[ \dot N_i(s)= \varphi_i(s)\geq 0, \qquad s\in [-\tau,0], \quad \varphi_i(0)> 0, \] \[ \varphi_i\in C([-\tau,0], [0,+\infty))\cap C^1([-\tau,0], [0,+\infty)), \quad i=1,\dots, n, \] where \(a_{ij}, b_{ij}\in C(\mathbb{R},(0,+\infty))\), \(r_i, \tau_{ij}\in C(\mathbb{R},\mathbb{R})\) are \(\omega\)-periodic functions and \(c_{ij}\), \(\sigma_{ij}\) are constants, \(c_{ij}\) are nonnegative. The goal of the author is to derive a set of easily verifiable sufficient conditions for the existence of periodic solutions of (1).
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2082136
zbMATH Keywords: neutral type
zbMATH Keywords: delay
zbMATH Keywords: periodic solution
zbMATH Keywords: coincidence degree
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.12.035
OpenAlex ID: W1995316592
cites work: Periodic solution of a periodic neutral delay equation
cites work: On a periodic neutral delay Lotka-Volterra system
cites work: Q4761540
cites work: Q3159535
cites work: Q4003237
cites work: On neutral-delay two-species Lotka-Volterra competitive systems
cites work: Ordinary differential equations with nonlinear boundary conditions
cites work: Existence and global attractivity of positive periodic solutions to periodic \(n\)-species Lotka-Volterra competition systems with several deviating arguments
DOI: 10.1016/J.JMAA.2003.12.035
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description: scientific article; zbMATH DE number 2082136