Existence of periodic solutions for delay differential equations with state dependent delay
type: Item
instance of: scholarly article
title: Existence of periodic solutions for delay differential equations with state dependent delay
zbMATH Open document ID: 0913.34057
author: D. Arino
author: Karl-Peter Hadeler
author: M. L. Hbid
published in: Journal of Differential Equations
publication date: 1999-05-24T00:00:00Z
review text: The existence of periodic solutions to a delay differential equation, with delay depending indirectly on the state, of the form \[ \frac {dx}{dt}=-f(x(t-\tau(t))), \quad\text{with}\quad \frac {d\tau}{dt}=h(x(t),\tau(t)) \] is studied. A fixed point problem related to a Poincaré operator is constructed and solved using an ejective fixed point theorem.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1206602
zbMATH Keywords: periodic solutions
zbMATH Keywords: delay differential equation
zbMATH Keywords: state dependent delay
reviewed by: Josef Diblík
MaRDI profile type: Publication
full work available at URL: jdeq.1997.3378
OpenAlex ID: W2021908089
cites work: Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay
cites work: A mathematical model of growth of population of fish in the larval stage: Density-dependence effects
cites work: More on ordinary differential equations which yield periodic solutions of delay differential equations
cites work: A further generalization of the Schauder fixed point theorem
cites work: Periodic solutions of autonomous equations
cites work: Q4000352
cites work: Periodic solutions of difference-differential equations
cites work: Q3860165
cites work: Introduction to functional differential equations
cites work: Q4027581
cites work: Boundary layer phenomena for differential-delay equations with state- dependent time lags. I
cites work: Periodic solutions for functional differential equations with multiple state-dependent time lags
cites work: Periodic solutions of some nonlinear autonomous functional differential equations
cites work: Q3892609
cites work: A non-linear difference-differential equation.
DOI: 10.1006/JDEQ.1997.3378
description: scientific article; zbMATH DE number 1206602