#### Mouataz Billah Mesmouli, Abdelouaheb Ardjouni, Ahcene Djoudi, Stability in neutral nonlinear differential equations, Vol. 2017 (2017), Article ID 4, pp. 1-17

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DOI: 10.23952/jnfa.2017.4

Received August 3, 2016; Accepted November 20, 2016

Abstract. In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton and the Carath\'{e}odory condition to obtain stability results of the zero solution of the neutral nonlinear differential equations with variable delay $x'(t)=-a(t)h(x(t))+c(t)x'(t-\tau(t))+G(t,x(t),x(t-\tau(t))).$ The stability of the zero solution of this eqution provided that $h\left(0\right) =G\left( t,0,0\right)=0$.