Journal of Dynamics and Differential Equations

, Volume 28, Issue 3–4, pp 1163–1186 | Cite as

Persistence and Permanence for a Class of Functional Differential Equations with Infinite Delay

  • Teresa FariaEmail author


The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with initial conditions that are positive, continuous and bounded. The present method applies to a very broad class of abstract systems of FDEs with infinite delay, both autonomous and non-autonomous, which include many important models used in mathematical biology. Moreover, the hypotheses imposed are in general very easy to check. The results are illustrated with some selected examples.


Infinite delay Persistence Permanence Quasimonotone condition Lotka–Volterra model 

AMS Subject Classification

34K12 34K25 92D25 



Work supported by Fundação para a Ciência e a Tecnologia, under UID/MAT/04561/2013.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de Matemática and CMAF-CIO, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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