Invariant Cones of Positive Initial Functions for Delay Differential Equations

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Consider the scalar delay differential equation [formula omitted] where ak and τk ≥ 0, (0 ≤ k ≤ m), are real numbers. In this paper we show that there exists an invariant cone of the positive initial functions if and only if the characteristic equation of Eq. (1) has a real root. We also give the constraction of the maximal invariant cone among the positive initial functions with respect to Eq. (1). At the end of the paper we show the generalizations of these results for systems.

Original languageEnglish
Pages (from-to)21-41
Number of pages21
JournalApplicable Analysis
Volume35
Issue number1-4
DOIs
Publication statusPublished - Jan 1 1990

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Invariant Cone
Delay Differential Equations
Cones
Differential equations
Maximal Invariant
Real Roots
Characteristic equation
Scalar
If and only if

Keywords

  • delay differential equations
  • existence of positive solutions
  • Invariant cones
  • monotone semiflows

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Invariant Cones of Positive Initial Functions for Delay Differential Equations. / Győri, I.

In: Applicable Analysis, Vol. 35, No. 1-4, 01.01.1990, p. 21-41.

Research output: Contribution to journalArticle

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