On the boundedness and periodicity of the solutions to a certain vector differential equation of third-order
type: Item
instance of: scholarly article
title: On the boundedness and periodicity of the solutions to a certain vector differential equation of third-order
zbMATH Open document ID: 0933.34058
DOI: 10.1007/BF02481895
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2000-03-29T00:00:00Z
review text: The third-order system of nonlinear differential equations \[ \dddot X+F(X,\dot X)\ddot X+B\dot X+H(X)=P(t,X,\dot X,\ddot X)\tag{1} \] is considered, with \(X\in\mathbb{R}^n\), \(F,H\) and \(P\) are continuous, \(B\) is a real constant symmetric \(n\times n\)-matrix and the dots denote differentiation with respect to \(t\). Sufficient conditions are established for the ultimate boundedness of solutions and for the existence of periodic solutions to (1).
Mathematics Subject Classification ID: 34D40
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1346265
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: ultimate boundedness
zbMATH Keywords: solutions
zbMATH Keywords: existence
zbMATH Keywords: periodic solutions
author: Cemil Tunç
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
Wikidata QID: Q115392120
cites work: Q5183880
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cites work: BOUNDEDNESS AND STABILITY PROPERTIES OF SOLUTIONS OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD
cites work: Q3864859
description: scientific article; zbMATH DE number 1346265