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

100%
Erman S., Demir A.
Open Mathematics
|
2016
|
tom 14
|
nr 1
425-435
EN
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.
2
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New oscillation criteria for first order nonlinear delay differential equations

100%
Tang X., Shen J.
Colloquium Mathematicum
|
2000
|
tom 83
|
nr 1
21-41
EN
New oscillation criteria are obtained for all solutions of a class of first order nonlinear delay differential equations. Our results extend and improve the results recently obtained by Li and Kuang [7]. Some examples are given to demonstrate the advantage of our results over those in [7].
3
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Logistic equations in tumour growth modelling

63%
Foryś U., Marciniak-Czochra A.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 3
317-325
EN
The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.
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