Dynamics of a second-order nonlinear equation with a large coefficient of delay control
type: Item
instance of: scholarly article
title: Dynamics of a second-order nonlinear equation with a large coefficient of delay control
zbMATH Open document ID: 1312.34113
DOI: 10.1134/S1064562414050287
published in: Doklady Mathematics
publication date: 2014-12-17T00:00:00Z
review text: The author studies the nonlinear second-order differential equation with delay control \[ \begin{aligned} \ddot U=F&(U,\dot U)+\lambda[\dot U(t-T)-\dot U] \\ +&\lambda\alpha[U(t-T)-U], \end{aligned} \] with a nonlinear function \(F,\) the delay coefficient \(T\) and the delay control coefficient \(\lambda,\) which is assumed to be positive and large, \(\alpha>0\) is a constant. Using the averaging principle and the principal asymptotic approximation techniques, an asymptotic expansion of the solutions for \(\epsilon=\lambda^{-1}\to 0^+\) is constructed.
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 34K33
Mathematics Subject Classification ID: 34K35
zbMATH DE Number: 6381293
zbMATH Keywords: second-order differential equation
zbMATH Keywords: delay
zbMATH Keywords: averaging
zbMATH Keywords: asymptotic representation
author: S. A. Kashchenko
MaRDI profile type: Publication
cites work: Q5435500
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description: scientific article; zbMATH DE number 6381293