Solution estimates for linear differential equations with delay

Leonid Berezansky and Elena Braverman

Applied Mathematics and Computation, 2020, vol. 372, issue C

Abstract: 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 equationx˙(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.

Keywords: Linear delay differential equations; Explicit solution estimates; Variable delays and coefficients; Exponential stability (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309543

DOI: 10.1016/j.amc.2019.124962

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