On stability and boundedness of solutions of a certain fourth-order delay differential equation
type: Item
instance of: scholarly article
title: On stability and boundedness of solutions of a certain fourth-order delay differential equation
zbMATH Open document ID: 0697.34063
DOI: 10.1155/S0161171289000724
author: Emmanuel O. Okoronkwo
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46458
review text: A Razumikhin-type theorem is used to obtain sufficient conditions for uniform asymptotic stability and boundedness of solutions of a fourth- order scalar delay-differential equation of the form \[ x^{''''}(t)+f(x''(t))x'''(t)+\alpha_ 2x''(t)+\beta_ 2x''(t- h)+g(x'(t-h))+\alpha_ 4x(t)+\beta_ 4x(t-h)=P(t). \] The proof utilizes a Lyapunov function obtained by \textit{J. O. C. Ezeilo} in study of a related ordinary differential equation [J. Math. Anal. Appl. 5, 136- 146 (1962; Zbl 0107.296)].
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 4142519
zbMATH Keywords: Razumikhin-type theorem
zbMATH Keywords: uniform asymptotic stability
zbMATH Keywords: boundedness of solutions
zbMATH Keywords: fourth-order scalar delay-differential equation
zbMATH Keywords: Lyapunov function
Wikidata QID: Q115243303
reviewed by: Louis J. Grimm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4142519