Abdelouaheb Ardjouni, Ahcene Djoudi, Imene Soualhia
Abstract:
In this article we study a linear neutral integro-differential equation with
variable delays and give suitable conditions to obtain asymptotic stability
of the zero solution, by means of fixed point technique.
An asymptotic stability theorem with a necessary and sufficient condition is
proved, which improves and generalizes previous results due to Burton [5],
Becker and Burton [4] and Jin and Luo [5].
We provide an example that illustrates our results.
Submitted June 20, 2012. Published October 12, 2012.
Math Subject Classifications: 34K20, 34K30, 34K40.
Key Words: Fixed point; stability; integro-differential equation;
variable delay.
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Abdelouaheb Ardjouni Applied Mathematics Lab., Facullty of Sciences Department of Mathematics, Badji Mokhtar University of Annaba P.O. Box 12, Annaba 23000, Algeria email: abd_ardjouni@yahoo.fr |
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| Ahcene Djoudi Applied Mathematics Lab., Facullty of Sciences Department of Mathematics, Badji Mokhtar University of Annaba P.O. Box 12, Annaba 23000, Algeria email: adjoudi@yahoo.com | |
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Imene Soualhia Applied Mathematics Lab., Facullty of Sciences Department of Mathematics, Badji Mokhtar University of Annaba P.O. Box 12, Annaba 23000, Algeria |
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