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

Feliz Minhós; Sara Perestrelo; Feliz Minhós; Sara Perestrelo

doi:10.3934/math.2023846

AIMS Mathematics

2023, Volume 8, Issue 7: 16542-16555. doi: 10.3934/math.2023846

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

Feliz Minhós ^1,2,
Sara Perestrelo ^{1,2
,
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1.
Department of Mathematics, School of Sciences and Technology, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
2.
Research Centre in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Portugal

Received: 28 February 2023 Revised: 28 April 2023 Accepted: 06 May 2023 Published: 10 May 2023
MSC : 34A34, 34B15, 34C25, 92D25

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.
- periodic nonlinear coupled systems,
- upper and lower solutions,
- periodic solutions,
- existence and localization result,
- population dynamics
Citation: Feliz Minhós, Sara Perestrelo. First-order periodic coupled systems with orderless lower and upper solutions[J]. AIMS Mathematics, 2023, 8(7): 16542-16555. doi: 10.3934/math.2023846

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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.

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