# An analysis on the stability of a state dependent delay differential equation

Open Mathematics (2016)

• Volume: 14, Issue: 1, page 425-435
• ISSN: 2391-5455

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## Abstract

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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t).$\tau \left(u\left(t\right)\right)=\frac{a+bu\left(t\right)}{c+bu\left(t\right)}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

## How to cite

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Sertaç Erman, and Ali Demir. "An analysis on the stability of a state dependent delay differential equation." Open Mathematics 14.1 (2016): 425-435. <http://eudml.org/doc/285500>.

@article{SertaçErman2016,
abstract = {In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac\{\{a + bu(t)\}\}\{\{c + bu(t)\}\}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.},
author = {Sertaç Erman, Ali Demir},
journal = {Open Mathematics},
keywords = {Asymptotic stability; state depended delay; delay differential equation; asymptotic stability; state dependent delay; existence and uniqueness},
language = {eng},
number = {1},
pages = {425-435},
title = {An analysis on the stability of a state dependent delay differential equation},
url = {http://eudml.org/doc/285500},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Sertaç Erman
AU - Ali Demir
TI - An analysis on the stability of a state dependent delay differential equation
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 425
EP - 435
AB - In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.
LA - eng
KW - Asymptotic stability; state depended delay; delay differential equation; asymptotic stability; state dependent delay; existence and uniqueness
UR - http://eudml.org/doc/285500
ER -

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