Solution estimates for linear differential equations with delay

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper, we give explicit exponential estimates |x(t)|≤Me−γ(t−t0), where t ≥ t0, M > 0, for solutions of a linear scalar delay differential equation x˙(t)+∑k=1mbk(t)x(hk(t))=f(t),t≥t0,x(t)=ϕ(t),t≤t0.We consider two different cases: when γ > 0 (corresponding to exponential stability) and the case of γ < 0 when the solution is, generally, growing. In the first case, together with the exponential estimate, we also obtain an exponential stability test, in the second case we get estimation for solution growth. Here both the coefficients and the delays are measurable, not necessarily continuous.

Original languageEnglish
Article number124962
JournalApplied Mathematics and Computation
StatePublished - 1 May 2020


  • Explicit solution estimates
  • Exponential stability
  • Linear delay differential equations
  • Variable delays and coefficients

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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