Convergence to equilibria in a differential equation with small delay

Pituk, Mihály. "Convergence to equilibria in a differential equation with small delay." Mathematica Bohemica 127.2 (2002): 293-299. <http://eudml.org/doc/249050>.

@article{Pituk2002,
abstract = {Consider the delay differential equation \[ \dot\{x\}(t)=g(x(t),x(t-r)), \qquad \mathrm \{(1)\}\] where $r>0$ is a constant and $g\:\mathbb \{R\}^2\rightarrow \mathbb \{R\}$ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.},
author = {Pituk, Mihály},
journal = {Mathematica Bohemica},
keywords = {delay differential equation; equilibrium; convergence; delay differential equation; equilibrium; convergence},
language = {eng},
number = {2},
pages = {293-299},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence to equilibria in a differential equation with small delay},
url = {http://eudml.org/doc/249050},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Pituk, Mihály
TI - Convergence to equilibria in a differential equation with small delay
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 293
EP - 299
AB - Consider the delay differential equation \[ \dot{x}(t)=g(x(t),x(t-r)), \qquad \mathrm {(1)}\] where $r>0$ is a constant and $g\:\mathbb {R}^2\rightarrow \mathbb {R}$ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
LA - eng
KW - delay differential equation; equilibrium; convergence; delay differential equation; equilibrium; convergence
UR - http://eudml.org/doc/249050
ER -