Periodic solutions of dissipative functional differential equations
type: Item
instance of: scholarly article
title: Periodic solutions of dissipative functional differential equations
zbMATH Open document ID: 0805.34059
author: Géza Makay
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-11-29T00:00:00Z
review text: In this paper we consider \(T\)-periodic finite delay differential equations. We investigate dissipativeness for these equations, which is a weaker condition than uniform ultimate boundedness. The later condition is usually used together with uniform boundedness to prove the existence of a \(T\)-periodic solution. The first two theorems prove dissipativeness for these equations generalizing a result of Pliss. Hale and Lopes proved a result that implies that a dissipative \(T\)-periodic finite delay equation has a \(T\)-periodic solution. Since this result is not very well known, we restate it and prove it in a short, elementary way. We also present a theorem using Lyapunov functionals to show the dissipativeness of a finite delay differential equation. We also give an example, which is dissipative but not uniformly ultimately bounded.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D40
zbMATH DE Number: 697063
zbMATH Keywords: periodic solutions
zbMATH Keywords: periodic finite delay differential equations
zbMATH Keywords: dissipativeness
zbMATH Keywords: uniform ultimate boundedness
zbMATH Keywords: Lyapunov functionals
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225721
OpenAlex ID: W2023076256
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DOI: 10.2748/TMJ/1178225721
description: scientific article; zbMATH DE number 697063