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Well-Posedness for a System of Integro-Differential Equations

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Abstract

We give sufficient conditions for the existence, the uniqueness and the continuous dependence on initial data of the solution to a system of integro-differential equations with superlinear growth on the nonlinear term. As possible applications of our methods we consider two epidemic models: a perturbed versions of the well-known integro-differential Kendall SIR model, and a SIRS-like model.

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Notes

  1. From condition (14) with \(C=\sigma -\rho /2\).

  2. From condition (16) with \(C= 2(\sigma -\rho /2)\).

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Acknowledgements

The authors are members of INdAM and GNAMPA. The paper was partially supported by the projects GNAMPA 2015 “Applicazioni di metodi topologici allo studio di problemi differenziali finalizzati all’analisi di modelli di fenomeni reali ” and “Dinamiche non autonome, sistemi hamiltoniani e teoria del controllo”.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    Irene Benedetti

  2. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Via S. Marta 3, 50139, Firenze, Italy

    Luca Bisconti

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  1. Irene Benedetti
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Correspondence to Irene Benedetti.

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Benedetti, I., Bisconti, L. Well-Posedness for a System of Integro-Differential Equations. Differ Equ Dyn Syst 28, 999–1013 (2020). https://doi.org/10.1007/s12591-017-0359-5

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