Stability in nonlinear neutral differential equations with infinite delay

In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the nonlinear neutral differential equation with infinite delay d/dt x(t) = -a(t) x (t - T1(t)) + d/dt Q (t, x (t - T2(t))) + ∫ D(t,s) f (x (s))ds. An asymptotic stability theorem with a necessary and suff...

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Bibliographic Details
Main Authors: Ardjouni Abdelouaheb, Djoudi Ahcene
Format: Article
Language:English
Published: University of Kragujevac, Faculty of Technical Sciences Čačak 2014-01-01
Series:Mathematica Moravica
Subjects:
Online Access:http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2014/1450-59321402091A.pdf
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Summary:In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the nonlinear neutral differential equation with infinite delay d/dt x(t) = -a(t) x (t - T1(t)) + d/dt Q (t, x (t - T2(t))) + ∫ D(t,s) f (x (s))ds. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton [6], Zhang [17], Althubiti, Makhzoum, Raffoul [1].
ISSN:1450-5932
2560-5542