# 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)
• Accepted : 2017.12.19
• Published : 2018.03.25
• 164 11

#### 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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