STABILITY BY KRASNOSELSKII'S THEOREM IN TOTALLY NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

被引：12
|
作者：
Derrardjia, Ishak [1 ]
Ardjouni, Abdelouaheb [1 ]
Djoudi, Ahcene [1 ]
机构：
[1] Univ Annaba, Dept Math, Fac Sci, POB 12, Annaba 23000, Algeria
来源：
OPUSCULA MATHEMATICA | 2013年 / 33卷 / 02期
关键词：
fixed point; stability; nonlinear neutral equation; Krasnoselskii-Burton theorem;
D O I：
10.7494/OpMath.2013.33.2.255
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：255 / 272
页数：18
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