Bound of solutions to third-order nonlinear differential equations with bounded delay
type: Item
instance of: scholarly article
title: Bound of solutions to third-order nonlinear differential equations with bounded delay
zbMATH Open document ID: 1193.34139
author: Cemil Tunç
published in: Journal of the Franklin Institute
publication date: 2010-04-15T00:00:00Z
review text: Consider the delay differential equation \[ \begin{multlined} x'''+ f(x,x',x'')+ g(x(t- r(t)), x'(t)- r(t))\\ +h(x(t- r(t)))= p(t,x,x',x(t- r(t)), x'(t- r(t)), x'')\end{multlined}\tag{\(*\)} \] under the assumption that the delay satisfies \[ 0\leq r(t)\leq\alpha,\quad r'(t)\leq\beta,\quad \alpha> 0,\quad 0<\beta< 1. \] The author gives additional conditions on \(f\), \(g\), \(h\), \(p\) such that the solution of the Cauchy problem of \((*)\) is uniformly bounded including its first and second derivative. The proof is based on the construction of a Lyapunov functional.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34K12
zbMATH DE Number: 5693306
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: third-order delay differential equation
MaRDI profile type: Publication
full work available at URL: j.jfranklin.2009.05.001
OpenAlex ID: W2077372953
cites work: Stability and periodic solutions of ordinary and functional differential equations
cites work: Q5343588
cites work: Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
cites work: Theory of functional differential equations. 2nd ed
cites work: Introduction to functional differential equations
cites work: Q4229393
cites work: Stability of functional differential equations
cites work: Q3845518
cites work: Stability of motion
cites work: Q5183880
cites work: Stability and boundedness of a kind of third-order delay differential system
cites work: Q5699790
cites work: Q3082748
cites work: Q3408087
cites work: Stability and boundedness properties of certain second-order differential equations
cites work: On the asymptotic behavior of solutions of certain second-order differential equations
cites work: On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument
cites work: Q5520199
cites work: Q4019173
DOI: 10.1016/J.JFRANKLIN.2009.05.001
description: scientific article; zbMATH DE number 5693306