On the global stability properties and boundedness results of solutions of third-order nonlinear differential equations
type: Item
instance of: scholarly article
title: On the global stability properties and boundedness results of solutions of third-order nonlinear differential equations
zbMATH Open document ID: 1397.34092
DOI: 10.1155/2013/103260
author: Muzaffer Ateş
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We studied the global stability and boundedness results of third-order nonlinear differential equations of the form \(\dddot{x}+\psi(x,\dot x,\ddot{x})\ddot{x}+f(x,\dot{x},\ddot{x})=P(t,x,\dot x,\ddot{x})\). Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with \(P\equiv 0\) and the other with \(P\neq 0\). The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 37B25
zbMATH DE Number: 6950510
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/103260
OpenAlex ID: W2061347978
Wikidata QID: Q59001595
DBLP publication ID: journals/jam/Ates13
description: scientific article; zbMATH DE number 6950510