Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 172, pp. 1-14.

Title: Stability for linear neutral integro-differential equations
       with variable delays

Authors: Abdelouaheb Ardjouni (Badji Mokhtar Univ. of Annaba, Algeria)
         Ahcene Djoudi        (Badji Mokhtar Univ. of Annaba, Algeria)
	 Imene Soualhia       (Badji Mokhtar Univ. of Annaba, Algeria)

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.