Electron. J. Diff. Equ., Vol. 2012 (2012), No. 172, pp. 1-14.

Stability for linear neutral integro-differential equations with variable delays

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
  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
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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