@Article{Derrardjia2013,
author = "Derrardjia, Ishak and Ardjouni, Abdelouaheb and Djoudi, Ahcene",
title = "Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "2",
pages = "255--272",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.2.255",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.2.255",
abstract = "In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study concerns \[x'(t)=a(t)x^3(t)+c(t)x'(t-r(t))+b(t)x^3(t-r(t)).\] The equation has proved very challenging in the theory of Liapunov's direct method. The stability results are obtained by means of Krasnoselskii-Burton's theorem and they improve on the work of T.A. Burton (see Theorem 4 in [Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem, Nonlinear Studies 9 (2001), 181-190]) in which he takes \(c=0\) in the above equation.",
keywords = "fixed point, stability, nonlinear neutral equation, Krasnoselskii-Burton theorem",
issn = "1232-9274"
}