Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument x‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory...

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Main Authors: Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/278962
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spelling doaj-34873465c50c4875be38d710941966fa2020-11-24T21:54:47ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/278962278962Oscillation for Third-Order Nonlinear Differential Equations with Deviating ArgumentMiroslav Bartušek0Mariella Cecchi1Zuzana Došlá2Mauro Marini3Department of Mathematics and Statistics, Masaryk University, CZ-61137 Brno, Czech RepublicDepartment of Electronic and Telecommunications, University of Florence, I-50139 Florence, ItalyDepartment of Mathematics and Statistics, Masaryk University, CZ-61137 Brno, Czech RepublicDepartment of Electronic and Telecommunications, University of Florence, I-50139 Florence, ItalyWe study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument x‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator ℒx=x‴+q(t)x′ is oscillatory.http://dx.doi.org/10.1155/2010/278962
collection DOAJ
language English
format Article
sources DOAJ
author Miroslav Bartušek
Mariella Cecchi
Zuzana Došlá
Mauro Marini
spellingShingle Miroslav Bartušek
Mariella Cecchi
Zuzana Došlá
Mauro Marini
Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
Abstract and Applied Analysis
author_facet Miroslav Bartušek
Mariella Cecchi
Zuzana Došlá
Mauro Marini
author_sort Miroslav Bartušek
title Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
title_short Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
title_full Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
title_fullStr Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
title_full_unstemmed Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument
title_sort oscillation for third-order nonlinear differential equations with deviating argument
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2010-01-01
description We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument x‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator ℒx=x‴+q(t)x′ is oscillatory.
url http://dx.doi.org/10.1155/2010/278962
work_keys_str_mv AT miroslavbartusek oscillationforthirdordernonlineardifferentialequationswithdeviatingargument
AT mariellacecchi oscillationforthirdordernonlineardifferentialequationswithdeviatingargument
AT zuzanadosla oscillationforthirdordernonlineardifferentialequationswithdeviatingargument
AT mauromarini oscillationforthirdordernonlineardifferentialequationswithdeviatingargument
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