Oscillation, convergence, and stability of linear delay differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:293

Article

Stavroulakis, John Ioannis¹  Braverman, Elena² 

[1] Natl Tech Univ Athens, Sch Appl Math & Phys Sci, Athens 15780, Greece

[2] Univ Calgary, Dept Math & Stats, Calgary, AB T2N 1N4, Canada

关键词: Stability;    First-order delay differential equation;    Oscillation;    Asymptotic behaviour;    Oscillating coefficient;   

DOI  :  10.1016/j.jde.2021.05.021

来源: Elsevier

【 摘 要 】

There is a close connection between stability and oscillation of delay differential equations. For the firstorder equation x'(t) + c(t)x(tau(t)) = 0, t >= 0, where cis locally integrable of any sign, tau(t) <= tis Lebesgue measurable, lim(t ->infinity) tau(t) = infinity, we obtain sharp results, relating the speed of oscillation and stability. We thus unify the classical results of Myshkis and Lillo. We also generalise the 3/2-stability criterion to the case of measurable parameters, improving 1 + 1/e to the sharp 3/2constant. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free