Explicit exponential stability conditions for linear differential equations with several delays

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

New explicit conditions of exponential stability are obtained for the nonautonomous linear equationover(x, ̇) (t) + underover(∑, k = 1, m) ak (t) x (hk (t)) = 0, where ∑k = 1m ak (t) ≥ 0, hk (t) ≤ t, by comparing this equation with a nonoscillatory exponentially stable equation of the formover(x, ̇) (t) + under(∑, k ∈ I) ak (t) x (gk (t)) = 0, where I ⊂ {1, ..., m}, gk (t) ≤ t. Every comparison result gives 2m - 1 different stability conditions due to the a priori choice of a subset I.

Original languageEnglish
Pages (from-to)246-264
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume332
Issue number1
DOIs
StatePublished - 1 Aug 2007

Keywords

  • Delay equations
  • Exponential stability
  • Positive fundamental function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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