Korean J. Math.  Vol 25, No 3 (2017)  pp.303-321
DOI: http://dx.doi.org/10.11568/kjm.2017.25.3.303

Stability in nonlinear neutral Levin-Nohel integro-differential equations

Kamel Ali Khelil, Abdelouaheb Ardjouni, Ahcene Djoudi

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


Fixed points, neutral integro-differential equations, stability

Subject classification

34K20, 34K30, 34k40.

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References


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