Monotone semiflows in scalar non-quasi-monotone functional differential equations

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Abstract

By introducing a stronger than pointwise ordering, conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi-monotone. Typically the maximum delay must be the smaller the more quasi-monotonicity is violated. The theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations.

Original languageEnglish (US)
Pages (from-to)289-306
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume150
Issue number2
DOIs
StatePublished - 1990

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Semiflow
Functional Differential Equations
Ordinary differential equations
Monotone
Differential equations
Scalar
Quasimonotonicity
Stability of Equilibria
Ordinary differential equation
Converge

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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title = "Monotone semiflows in scalar non-quasi-monotone functional differential equations",
abstract = "By introducing a stronger than pointwise ordering, conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi-monotone. Typically the maximum delay must be the smaller the more quasi-monotonicity is violated. The theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations.",
author = "Hal Smith and Horst Thieme",
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AB - By introducing a stronger than pointwise ordering, conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi-monotone. Typically the maximum delay must be the smaller the more quasi-monotonicity is violated. The theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations.

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