Periodic solutions of a $2$-dimensional system of neutral difference equations

Małgorzata Migda; Ewa Schmeidel; Małgorzata Zdanowicz

doi:10.3934/dcdsb.2018024

Article Contents

2018, Volume 23, Issue 1: 359-367. Doi: 10.3934/dcdsb.2018024

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Periodic solutions of a $2$-dimensional system of neutral difference equations

1.
Poznan University of Technology, Piotrowo 3A, 60-965 Poznań, Poland
2.
University of Bialystok, K. Ciołkowskiego 1M, 15-245 Białystok, Poland

* Corresponding author: Ma lgorzata Zdanowicz
* Corresponding author: Ma lgorzata Zdanowicz

Received: August 31, 2016

Revised: April 30, 2017

Published: November 2017

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Abstract

The 2-dimensional system of neutral type nonlinear difference equations with delays in the following form

$\left\{ \begin{align}&Δ≤(x_1(n)-p_1(n)\,x_1(n-τ_1))=a_1(n)\,f_1(x_1(n-σ_1),x_2(n-σ_2))\\&Δ≤(x_2(n)-p_2(n)\,x_2(n-τ_2))=a_2(n)\,f_2(x_1(n-σ_3),x_2(n-σ_4)),\end{align} \right.$

is considered. In this paper we use Schauder's fixed point theorem to study the existence of periodic solutions of the above system.

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Mathematics Subject Classification: Primary: 39A10; Secondary: 39A23.

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References

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