# 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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topSertaç 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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