Multiple positive periodic solutions for delay differential system
type: Item
instance of: scholarly article
title: Multiple positive periodic solutions for delay differential system
zbMATH Open document ID: 1201.34106
DOI: 10.1155/2009/239209
author: Zhaocai Hao
author: Ti-Jun Xiao
author: Jin Liang
published in: Discrete Dynamics in Nature and Society
publication date: 2010-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/233507
review text: The authors study the following general non-autonomous delay differential systems \[ \dot y_i(t)=-a_i(t)y_i(t)+f_i(t,\Upsilon_1(t), \Upsilon_2(t),\dots,\Upsilon_m(t)),\quad i=1,2,\dots,m\tag{1} \] and \[ \dot y_i(t)=a_i(t)y_i(t)-f_i(t,\Upsilon_1(t), \Upsilon_2(t),\dots,\Upsilon_m(t)),\quad i=1,2,\dots,m, \tag{2} \] where \[ \Upsilon_i(t):=(y_i(t-\tau_1(t)), y_i(t-\tau_2(t)), \dots, y_i(t-\tau_n(t))), \;t\in\mathbb R, \;i\in \Lambda_1=\{1,2,\dots,m\} \] and \(a_i, f_i\) \((i\in \Lambda_1)\) and \(\tau_j\) \((j\in \Lambda_2=\{1,2,\dots,n\})\) are given functions, here \(a_i\in C(\mathbb R,[0,\infty)),\) \(a_i(t)\not\equiv 0\), \(a_i(t)=a_i(t+T)\), \(t\in\mathbb R\), \(i\in \Lambda_1\), \(T>0\) is a fixed constant; \(f_i\in C(\mathbb R\times[0,\infty)^{m\times n},[0,\infty))\), \(i\in \Lambda_1\); \(f_i (i\in \Lambda_1)\) are \(T\)-periodic functions \(t\); \(\tau_j\in C(R,[0,\infty))\), \(\tau_j(t+T)=\tau_j(t)\), \(t\in\mathbb R\), \(j\in \Lambda_2\). By using multiple fixed-point theorems, the existence of multiple positive periodic solutions of the systems (1) and (2) is derived. Some examples are given to illustrate the main results.
reviewed by: Rui Xu
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5701457
zbMATH Keywords: periodic solution
zbMATH Keywords: delay
Wikidata QID: Q58647429
MaRDI profile type: Publication
OpenAlex ID: W2154377607
cites work: Q4003237
cites work: Delay differential equations: with applications in population dynamics
cites work: Global Stability of a Biological Model with Time Delay
cites work: Existence of periodic solutions of autonomous functional differential equations
cites work: Oscillation and Chaos in Physiological Control Systems
cites work: Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
cites work: On a periodic neutral logistic equation
cites work: On a neutral delay logistic equation
cites work: Positive periodic solution for a nonautonomous delay differential equation
cites work: Q3027941
cites work: Two positive fixed points of nonlinear operators on ordered Banach spaces
cites work: Q3854213
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description: scientific article; zbMATH DE number 5701457