On the existence of positive periodic solutions for second-order functional differential equations with multiple delays
type: Item
instance of: scholarly article
title: On the existence of positive periodic solutions for second-order functional differential equations with multiple delays
zbMATH Open document ID: 1260.34136
DOI: 10.1155/2012/929870
author: Qiang Li
author: Yongxiang Li
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: Existence results for positive \(\omega\)-periodic solutions are obtained for the second-order functional differential equation with multiple delays \[ u''(t) + a(t)u(t) = f(t, u(t), u(t - \tau_1(t)), \dots, u(t - \tau_n(t))), \] where \(a \in C(\mathbb R)\) is a positive \(\omega\)-periodic function, \(f : \mathbb R \times [0, +\infty)^{n+1} \rightarrow [0, +\infty)\) is a continuous function which is \(\omega\)-periodic in \(t\), and \(\tau_1(t), \dots, \tau_n(t) \in C(\mathbb R, [0, +\infty))\) are \(\omega\)-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary value problem. Our discussion is based on the fixed-point index theory in cones.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6134195
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/929870
OpenAlex ID: W2163795849
Wikidata QID: Q58697110
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description: scientific article; zbMATH DE number 6134195