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April 2021 Existence and uniqueness of periodic solutions in neutral nonlinear summation-difference systems with infinite delay
Abderrahim Guerfi, Abdelouaheb Ardjouni
Rocky Mountain J. Math. 51(2): 527-537 (April 2021). DOI: 10.1216/rmj.2021.51.527

Abstract

We use Krasnoselskii’s fixed point theorem to show that the neutral nonlinear summation-difference system with infinite delay Δx(n)=P(n)+A(n)x(nτ(n))+ΔQ(n,x(ng(n)))+k=nD(n,k)f(x(k)) has a periodic solution. We also use the contraction mapping principle to show that the periodic solution is unique. An example is given to illustrate our results.

Citation

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Abderrahim Guerfi. Abdelouaheb Ardjouni. "Existence and uniqueness of periodic solutions in neutral nonlinear summation-difference systems with infinite delay." Rocky Mountain J. Math. 51 (2) 527 - 537, April 2021. https://doi.org/10.1216/rmj.2021.51.527

Information

Received: 10 April 2020; Revised: 10 September 2020; Accepted: 17 September 2020; Published: April 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.527

Subjects:
Primary: 39A23
Secondary: 39A12

Keywords: contraction , fundamental matrix solution , Krasnoselskii's theorem , neutral difference equation , periodic solution

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 2 • April 2021
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