Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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STABILITY IN NONLINEAR NEUTRAL LEVIN-NOHEL INTEGRO-DIFFERENTIAL EQUATIONS

  • Received : 2017.03.09
  • Accepted : 2017.08.09
  • Published : 2017.09.30
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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 $$x^{\prime}(t)+{\displaystyle\smashmargin{2}{\int\nolimits_{t-{\tau}(t)}}^t}a(t,s)g(x(s))ds+c(t)x^{\prime}(t-{\tau}(t))=0$$. The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi [20].

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References

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