Nonoscillation and exponential stability of delay differential equations with oscillating coefficients

L. Berezansky, E. Braverman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We prove that under some additional conditions, the nonoscillation of the scalar delay differential equation ẋ(t) + ∑ k=1 m a k (t)x(h k(t)) = 0 implies the exponential stability. New nonoscillation conditions are obtained for equations with positive and negative coefficients and for equations of arbitrary signs. As an example, we present an exponentially stable equation with two delays and two oscillating coefficients.

Original languageEnglish
Pages (from-to)63-82
Number of pages20
JournalJournal of Dynamical and Control Systems
Volume15
Issue number1
DOIs
StatePublished - 14 Jan 2009

Keywords

  • Exponential stability
  • Linear delay equations
  • Oscillating coefficients
  • Positive fundamental function

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