Uniform Persistence in Functional Differential Equations

H. I. Freedman, Shigui Ruan

Research output: Contribution to journalArticle

137 Citations (Scopus)

Abstract

In this paper, we investigate the question of uniform persistence for retarded functional differential equations. By utilizing Liapunov-like functions, Razumikhin techniques, and differential inequalities, we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations, difference equations, and reaction-diffusion equations. We apply these criteria to some well known biological models with delay. Our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence. Moreover, these conditions are equivalent to uniform persistence for the cases without delay as well.

Original languageEnglish (US)
Pages (from-to)173-192
Number of pages20
JournalJournal of Differential Equations
Volume115
Issue number1
DOIs
StatePublished - Jan 1 1995
Externally publishedYes

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Uniform Persistence
Difference equations
Functional Differential Equations
Ordinary differential equations
Differential equations
Razumikhin Technique
Retarded Functional Differential Equations
Biological Models
Differential Inequalities
Reaction-diffusion Equations
Difference equation
Ordinary differential equation
Interior

ASJC Scopus subject areas

  • Analysis

Cite this

Uniform Persistence in Functional Differential Equations. / Freedman, H. I.; Ruan, Shigui.

In: Journal of Differential Equations, Vol. 115, No. 1, 01.01.1995, p. 173-192.

Research output: Contribution to journalArticle

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