### Stability in nonlinear neutral Levin-Nohel integro-differential equations

#### Abstract

In this paper we use the Krasnoselskii-Burton's fixed point theorem to obtain asymptotic stability and stability results about the zero solution for the following nonlinear neutral Levin-Nohel integro-differential equation

$$

x^{\prime }(t)+\int_{t-\tau (t)}^{t}a(t,s)g\left( x(s)\right)

ds+c(t)x^{\prime }(t-\tau (t))=0.

$$

The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi [20].

#### Keywords

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DOI: http://dx.doi.org/10.11568/kjm.2017.25.3.303

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