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Existence and uniqueness of periodic solutions for a system of nonlinear neutral functional differential equations with two functional delays

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Abstract

In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations

$$\begin{aligned} \frac{d}{dt}x\left( t\right) =A\left( t\right) x\left( t-\tau \left( t\right) \right) +\frac{d}{dt}Q\left( t,x\left( t-g\left( t\right) \right) \right) +G\left( t,x\left( t\right) ,x\left( t-g\left( t\right) \right) \right) \!. \end{aligned}$$

By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. Our results extend and complement some earlier publications.

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Authors and Affiliations

  1. Applied Mathematics Laboratory, Department of Mathematics, Faculty of Sciences, Univ Annaba, P.O. Box 12, Annaba, 23000, Algeria

    Mouataz Billah Mesmouli, Abdelouaheb Ardjouni & Ahcene Djoudi

  2. Department of Mathematics and Informatics, Faculty of Sciences and Technology, Univ Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria

    Abdelouaheb Ardjouni

Authors
  1. Mouataz Billah Mesmouli
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  2. Abdelouaheb Ardjouni
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  3. Ahcene Djoudi
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Correspondence to Abdelouaheb Ardjouni.

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Mesmouli, M.B., Ardjouni, A. & Djoudi, A. Existence and uniqueness of periodic solutions for a system of nonlinear neutral functional differential equations with two functional delays. Rend. Circ. Mat. Palermo 63, 409–424 (2014). https://doi.org/10.1007/s12215-014-0162-x

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  • DOI: https://doi.org/10.1007/s12215-014-0162-x

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