Honam Mathematical Journal (호남수학학술지)

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PERIODICITY AND POSITIVITY IN NEUTRAL NONLINEAR LEVIN-NOHEL INTEGRO-DIFFERENTIAL EQUATIONS

  • Bessioud, Karima (Department of Mathematics, Faculty of Sciences, University of Annaba) ;
  • Ardjouni, Abdelouaheb (Department of Mathematics and Informatics, University of Souk Ahras) ;
  • Djoudi, Ahcene (Applied Mathematics Lab, Department of Mathematics, Faculty of Sciences, University of Annaba)
  • Received : 2020.02.21
  • Accepted : 2020.10.01
  • Published : 2020.12.25
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Abstract

Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.

Keywords

Acknowledgement

The authors would like to thank the anonymous referee for his/her valuable comments and good advice.

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