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

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.

Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model

“…Recently, coupled systems have been studied by many authors, not only from a theoretical point of view but also due to the huge applications in many sciences and fields, with several methods and approaches. We recommend to the interested readers, for instance, [29][30][31][32][33][34][35][36][37][38][39].…”