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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.3 Antofagasta set. 2015

http://dx.doi.org/10.4067/S0716-09172015000300005 

 

Asymptotic stability in totally nonlinear neutral difference equations

 

Abdelouaheb Ardjouni

University Souk Ahras

Ahcene Djoudi

University Annaba, Algeria.


ABSTRACT

In this paper we use fixed point method to prove asymptotic stability results of the zero solution of the totally nonlinear neutral difference equation with variable delay

∆ x (n) = —a (n) f (x (n — τ (n))) + ∆g (n, x (n — τ (n))).

An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (2006) [23], Yankson (2009) [27], Jin and Luo (2009) [17] and Chen (2013) [9].

Subjclass [2000] : 39A30, 39A70.

Keywords : Fixed point, Stability, Neutral difference equations, Variable delay.


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Abdelouaheb Ardjouni

Faculty of Sciences and Technology,

Department of Mathematics and Informatics,

University Souk Ahras,

P. O. Box 1553,

Souk Ahras, 41000,

Algeria

e-mail: abd_ardjouni@yahoo.fr

Ahcene Djoudi

Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University Annaba,

P. O. Box 12, Annaba 23000, Algeria

e-mail: adjoudi@yahoo.com

Received : February 2015. Accepted : July 2015

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