PreprintCC BY 4.0arXiv
On exponential stability of generalized linear functional differential equations
Abstract
We develop a general approach to uniform exponential stability for a broad class of linear functional differential equations with Volterra operators. The considered class includes delay differential equations, integro-differential equations, equations with distributed delays, vector equations, and systems of scalar functional differential equations. Standard assumptions on the equation are relaxed to include measurable parameters. Some results remain valid for equations with unbounded delays and oscillatory coefficients and kernels. For all the above mentioned classes of equations, explicit uniform exponential stability tests are obtained.
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BibTeX
@misc{berezansky2026exponential,
title = {{On exponential stability of generalized linear functional differential equations}},
author = {Leonid Berezansky and Elena Braverman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22696},
eprint = {2610.22696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22696},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On exponential stability of generalized linear functional differential equations
AU - Leonid Berezansky
AU - Elena Braverman
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22696
UR - https://arxiv.org/abs/2610.22696
AB - We develop a general approach to uniform exponential stability for a broad class of linear functional differential equations with Volterra operators. The considered class includes delay differential equations, integro-differential equations, equations with distributed delays, vector equations, and systems of scalar functional differential equations. Standard assumptions on the equation are relaxed to include measurable parameters. Some results remain valid for equations with unbounded delays and oscillatory coefficients and kernels. For all the above mentioned classes of equations, explicit uniform exponential stability tests are obtained.
ER -