J. Nonl. Evol. Equ. Appl. 2013 (7), pp. 89-100, published on August 22, 2014:

Stability in nonlinear neutral Volterra difference equations with variable delays

A. Ardjouni, A. Djoudi

Department of Mathematics, Faculty of Sciences; University of Annaba, P.O. Box 12 Annaba, Algeria

Received on March 21, 2013
Accepted on August 30, 2013

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra difference equation with variable delays. Some conditions which allow the coefficient sequences to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a sufficient condition is proved. The obtained results improve and generalize those due to Raoul (2006), Yankson (2009) and Yankson (2006).
Keywords: Fixed point, Stability, Neutral Volterra difference equations, Variable delays.
2010 Mathematics Subject Classification:   39A30, 39A70.

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