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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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Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

76%
Baliki A., Benchohra M.
Nonautonomous Dynamical Systems
|
2014
|
tom 1
|
nr 1
EN
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
3
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On stability and robust stability of positive linear Volterra equations in Banach lattices

76%
Murakami S., Ngoc P.
Open Mathematics
|
2010
|
tom 8
|
nr 5
966-984
EN
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
4
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Ulam stability for a delay differential equation

76%
Otrocol D., Ilea V.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1296-1303
EN
We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given.
5
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Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

76%
Lu L., Lian Y., Li C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
218-232
EN
This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.
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