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Research Article | Open Access

First-order periodic coupled systems with orderless lower and upper solutions

Feliz Minhós1,2, Sara Perestrelo1,2( )
Department of Mathematics, School of Sciences and Technology, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Research Centre in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Portugal
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Abstract

We present some existence and localization results for periodic solutions of first-order coupled nonlinear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder's fixed point theorem together with not necessarily well-ordered upper and lower solutions. A real-case scenario shows the applicability of our results to some population dynamics models, describing the interaction between a criminal and a non-criminal population with a law enforcement component.

Keywords

periodic nonlinear coupled systemsupper and lower solutionsperiodic solutionsexistence and localization resultpopulation dynamics
CLC number: 34A34, 34B15, 34C25, 92D25

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16542-16555
DOI: 10.3934/math.2023846

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Cite this article:
Minhós F, Perestrelo S. First-order periodic coupled systems with orderless lower and upper solutions. AIMS Mathematics, 2023, 8(7): 16542-16555. https://doi.org/10.3934/math.2023846

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Received: 28 February 2023
Revised: 28 April 2023
Accepted: 06 May 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)