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http://dx.doi.org/10.5831/HMJ.2018.40.1.1

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS OF FIRST-ORDER NEUTRAL DIFFERENTIAL EQUATIONS  

Rezaiguia, Ali (Department of Mathematics and Informatics, University of Souk Ahras)
Ardjouni, Abdelouaheb (Department of Mathematics and Informatics, University of Souk Ahras)
Djoudi, Ahcene (Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba)
Publication Information
Honam Mathematical Journal / v.40, no.1, 2018 , pp. 1-11 More about this Journal
Abstract
We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].
Keywords
First-order neutral differential equations; Krasnoselski fixed point theorem; variable delay; positive periodic solutions;
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