TY - JOUR

T1 - Stability of Solutions of Delay Differential Equations

AU - Yskak, T.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project No. FWNF-2022-0008). Публикация для корректировки.

PY - 2023/8

Y1 - 2023/8

N2 - In the present article, we consider a class of systems of linear differential equations withinfinite distributed delay and periodic coefficients. We use the Lyapunov–Krasovskiĭfunctional and obtain sufficient conditions for exponential stability of the zero solution, findconditions on perturbation of the coefficients of the system that guarantee preservation ofexponential stability, and establish estimates for the norms of solutions of the initial andperturbed systems that characterize exponential decay at infinity.

AB - In the present article, we consider a class of systems of linear differential equations withinfinite distributed delay and periodic coefficients. We use the Lyapunov–Krasovskiĭfunctional and obtain sufficient conditions for exponential stability of the zero solution, findconditions on perturbation of the coefficients of the system that guarantee preservation ofexponential stability, and establish estimates for the norms of solutions of the initial andperturbed systems that characterize exponential decay at infinity.

KW - Lyapunov–Krasovskii functional

KW - linear differential equations with distributed delay

KW - periodic coefficients

KW - stability

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85169687377&origin=inward&txGid=f0ce71e94453edee7658f384ebffc89f

UR - https://www.mendeley.com/catalogue/86c75e95-f04e-3d42-8947-0a9037c68c61/

U2 - 10.1134/S1055134423030094

DO - 10.1134/S1055134423030094

M3 - Article

VL - 33

SP - 253

EP - 260

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -