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Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations

Authors :
Gennadii V. Demidenko
Inessa I. Matveeva
Source :
Mathematics, Vol 9, Iss 16, p 1847 (2021)
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

We consider a class of second-order nonlinear delay differential equations with periodic coefficients in linear terms. We obtain conditions under which the zero solution is asymptotically stable. Estimates for attraction sets and decay rates of solutions at infinity are established. This class of equations includes the equation of vibrations of the inverted pendulum, the suspension point of which performs arbitrary periodic oscillations along the vertical line.

Details

Language :
English
ISSN :
22277390
Volume :
9
Issue :
16
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.033899ec49ff4729b9ac6542a8958b0f
Document Type :
article
Full Text :
https://doi.org/10.3390/math9161847