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Journal of Dynamics and Differential Equations

, Volume 31, Issue 3, pp 1223–1245 | Cite as

Existence of Positive Periodic Solutions for Scalar Delay Differential Equations with and without Impulses

  • Teresa FariaEmail author
  • José J. Oliveira
Article
  • 264 Downloads

Abstract

The paper is concerned with a broad family of scalar periodic delay differential equations with linear impulses, for which the existence of a positive periodic solution is established under very general conditions. The proofs rely on fixed point arguments, employing either the Schauder theorem or Krasnoselskii fixed point theorem in cones. The results are illustrated with applications to an impulsive hematopoiesis model or generalized Nicholson’s equations, among other selected examples from mathematical biology. The method presented here turns out to be very powerful, in the sense that the derived theorems largely generalize and improve other results in recent literature, even for the situation without impulses.

Keywords

Delay differential equation Impulses Positive periodic solution Fixed point theorems Hematopoiesis model Nicholson equation 

Mathematics Subject Classification

34K13 34K45 92D25 

Notes

Acknowledgements

This work was partially supported by Fundação para a Ciência e a Tecnologia under Project UID/MAT/04561/2013 (Teresa Faria) and UID/MAT/00013/2013 (José J. Oliveira). The authors thank the referee, for bringing to their attention some relevant recent references. They also express their gratitude to the Editorial Board of this journal, for preparing a Special Issue in memory of Professor George Sell.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Departamento de Matemática and CMAF-CIO, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  2. 2.CMAT and Departamento de Matemática e Aplicações, Escola de CiênciasUniversidade do MinhoBragaPortugal

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