Geodesic
Stability in totally nonlinear neutral differential equations with variable delay
Abdelouaheb Ardjouni1 ; I. Derrardjia ; A. Djoudi ; Abdelouaheb Ardjouni ; I. Derrardjia ; A. Djoudi
1Department of Mathematics and Informatics, Mohamed Chérif Messaadia University of Souk-Ahras
Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 1, pp. 119-134 
Abdelouaheb Ardjouni; I. Derrardjia; A. Djoudi; Abdelouaheb Ardjouni; I. Derrardjia; A. Djoudi. Stability in totally nonlinear neutral differential equations with variable delay. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 1, pp. 119-134. http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a9/
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     author = {Abdelouaheb Ardjouni and I. Derrardjia and A. Djoudi and Abdelouaheb Ardjouni and I. Derrardjia and A. Djoudi},
     title = { Stability in totally nonlinear neutral differential equations with variable delay},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {119--134},
     year = {2014},
     volume = {83},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_1_a9/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper, we use a fixed point technique and the concept of large contractions to prove asymptotic stability results of the zero solution of a class of the totally nonlinear neutral differential equation with functional delay. The study concerns the equation$$x'(t) =- a (t)h(x(t)) + c(t)x'(t - r(t)) + b(t)G(x(t),x(t - r(t))),$$which 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 and generalize the works of Burton [7], and Derrardjia, Ardjouni and Djoudi [16].