TY - JOUR
T1 - Solution estimates for linear differential equations with delay
AU - Berezansky, Leonid
AU - Braverman, Elena
N1 - Funding Information:
The second author acknowledges the support of NSERC , the grant RGPIN-2015-05976 . Both authors are grateful to the reviewer for valuable comments and suggestions.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
KW - Explicit solution estimates
KW - Exponential stability
KW - Linear delay differential equations
KW - Variable delays and coefficients
UR - http://www.scopus.com/inward/record.url?scp=85077073616&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2019.124962
DO - 10.1016/j.amc.2019.124962
M3 - Article
AN - SCOPUS:85077073616
SN - 0096-3003
VL - 372
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 124962
ER -