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Axioms 2019, 8(1), 23; https://doi.org/10.3390/axioms8010023

First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model

1,2,* and 2,3
1
Department of Mathematics, British University of Vietnam, Ecopark Campus, 160000 Hung Yen, Hanoi, Vietnam
2
Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
3
Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora, 7000-812 Évora, Portugal
*
Author to whom correspondence should be addressed.
Received: 6 January 2019 / Revised: 13 February 2019 / Accepted: 13 February 2019 / Published: 16 February 2019
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
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Abstract

The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundary conditions. Functional boundary conditions, which are becoming increasingly popular in the literature, as they generalize most of the classical cases and in addition can be used to tackle global conditions, such as maximum or minimum conditions. The arguments used are based on the Arzèla Ascoli theorem and Schauder’s fixed point theorem. The existence results are directly applied to an epidemic SIRS (Susceptible-Infectious-Recovered-Susceptible) model, with global boundary conditions. View Full-Text
Keywords: coupled nonlinear systems; functional boundary conditions; Schauder’s fixed point theory; Arzèla Ascoli theorem; lower and upper solutions; first order periodic systems; SIRS epidemic model; mathematical modelling coupled nonlinear systems; functional boundary conditions; Schauder’s fixed point theory; Arzèla Ascoli theorem; lower and upper solutions; first order periodic systems; SIRS epidemic model; mathematical modelling
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Fialho, J.; Minhós, F. First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model. Axioms 2019, 8, 23.

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