On the qualitative behavior of solutions of third order differential equations
type: Item
instance of: scholarly article
title: On the qualitative behavior of solutions of third order differential equations
zbMATH Open document ID: 0856.34034
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-02-27T00:00:00Z
review text: The paper presents an important contribution to the qualitative theory of third-order differential equations of the form \[ \Biggl[ {1\over p(t)} \Biggl({1\over r(t)} x'\Biggr)'\Biggr]'+ q(t) x= 0,\tag \(E_1\) \] where \(p\), \(r\), \(q\) are twice differentiable functions with \(p(t)\neq 0\), \(r(t)\neq 0\), \(q(t)\neq 0\) for \(t\in [0, \infty)\). Some criteria on the structure of the space of solutions of equation \((E_1)\) are derived and some conditions concerning oscillation and nonoscillation of solutions of \((E_1)\) and other results are given. All the conditions are presented as integral criteria and involve only the integral behavior of the functions \(p\), \(r\), \(q\) on \([0, \infty)\). The obtained results generalize many results of other papers.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 902470
zbMATH Keywords: qualitative theory of third-order differential equations
zbMATH Keywords: oscillation
zbMATH Keywords: nonoscillation
author: M. Cecchi
author: Zuzana Došlá
author: Mauro Marini
author: Gabriele Villari
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0050
OpenAlex ID: W2000049092
DOI: 10.1006/JMAA.1996.0050
description: scientific article; zbMATH DE number 902470