Fourth-Order Differential Equation with Deviating Argument

Fourth-Order Differential Equation with Deviating Argument

We consider the fourth-order differential equation with middle-term and deviating argument x(4)(t)+q(t)x(2)(t)+r(t)f(x(φ(t)))=0, in case when the corresponding second-order equation h″+q(t)h=0 is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotical...

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Main Authors: M. Bartušek, M. Cecchi, Z. Došlá, M. Marini
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/185242
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spelling doaj-50ac58b4c36c437ea73edca55e0e70882020-11-24T21:33:56ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/185242185242Fourth-Order Differential Equation with Deviating ArgumentM. Bartušek0M. Cecchi1Z. Došlá2M. Marini3Department of Mathematics and Statistics, Masaryk University, 61137 Brno, Czech RepublicDepartment of Electronics and Telecommunications, University of Florence, 50139 Florence, ItalyDepartment of Mathematics and Statistics, Masaryk University, 61137 Brno, Czech RepublicDepartment of Electronics and Telecommunications, University of Florence, 50139 Florence, ItalyWe consider the fourth-order differential equation with middle-term and deviating argument x(4)(t)+q(t)x(2)(t)+r(t)f(x(φ(t)))=0, in case when the corresponding second-order equation h″+q(t)h=0 is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given. The roles of the deviating argument and the nonlinearity are explained, too.http://dx.doi.org/10.1155/2012/185242
collection DOAJ
language English
format Article
sources DOAJ
author M. Bartušek
M. Cecchi
Z. Došlá
M. Marini
spellingShingle M. Bartušek
M. Cecchi
Z. Došlá
M. Marini
Fourth-Order Differential Equation with Deviating Argument
Abstract and Applied Analysis
author_facet M. Bartušek
M. Cecchi
Z. Došlá
M. Marini
author_sort M. Bartušek
title Fourth-Order Differential Equation with Deviating Argument
title_short Fourth-Order Differential Equation with Deviating Argument
title_full Fourth-Order Differential Equation with Deviating Argument
title_fullStr Fourth-Order Differential Equation with Deviating Argument
title_full_unstemmed Fourth-Order Differential Equation with Deviating Argument
title_sort fourth-order differential equation with deviating argument
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We consider the fourth-order differential equation with middle-term and deviating argument x(4)(t)+q(t)x(2)(t)+r(t)f(x(φ(t)))=0, in case when the corresponding second-order equation h″+q(t)h=0 is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given. The roles of the deviating argument and the nonlinearity are explained, too.
url http://dx.doi.org/10.1155/2012/185242
work_keys_str_mv AT mbartusek fourthorderdifferentialequationwithdeviatingargument
AT mcecchi fourthorderdifferentialequationwithdeviatingargument
AT zdosla fourthorderdifferentialequationwithdeviatingargument
AT mmarini fourthorderdifferentialequationwithdeviatingargument
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