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

Hal Smith, Horst Thieme

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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
Issue number2
StatePublished - Aug 1990

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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