ON EXPONENTIAL STABILITY OF LINEAR DELAY EQUATIONS WITH OSCILLATORY COEFFICIENTS AND KERNELS

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

Abstract

New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation x (t) + ∑k=1m ak(t)x(hk(t)) + ∫g(t)t K(t, s)x(s)ds = 0, where hk(t) ≤ t, g(t) ≤ t, ak(•) and the kernel K(•, •) are oscillatory and, generally, discontinuous functions. The proofs are based on establishing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.

Original languageEnglish
Pages (from-to)559-580
Number of pages22
JournalDifferential and Integral Equations
Volume35
Issue number9-10
StatePublished - 1 Sep 2022

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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