Dynamics of Third-Order Nonlinear Neutral Equations

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form (r(t)([xt+∫abpt,μxτt,μdμ]′′)α)′+∫cdqt,ξfαxgt,ξdξ=0. Applying suitable generalized Riccati transformation and integral averaging techn...

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Main Authors: Hua Wang, Li Liu, Yanxiang Tan
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/917913
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author Hua Wang
Li Liu
Yanxiang Tan
author_facet Hua Wang
Li Liu
Yanxiang Tan
author_sort Hua Wang
collection DOAJ
description The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form (r(t)([xt+∫abpt,μxτt,μdμ]′′)α)′+∫cdqt,ξfαxgt,ξdξ=0. Applying suitable generalized Riccati transformation and integral averaging technique, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equation. Obtained results essentially improve and complement earlier ones.
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spelling doaj-art-b8ca7ecb49c541cd8b7425f67e372b9c2025-08-20T03:22:49ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/917913917913Dynamics of Third-Order Nonlinear Neutral EquationsHua Wang0Li Liu1Yanxiang Tan2School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410114, ChinaSchool of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410114, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, ChinaThe aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form (r(t)([xt+∫abpt,μxτt,μdμ]′′)α)′+∫cdqt,ξfαxgt,ξdξ=0. Applying suitable generalized Riccati transformation and integral averaging technique, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equation. Obtained results essentially improve and complement earlier ones.http://dx.doi.org/10.1155/2014/917913
spellingShingle Hua Wang
Li Liu
Yanxiang Tan
Dynamics of Third-Order Nonlinear Neutral Equations
Discrete Dynamics in Nature and Society
title Dynamics of Third-Order Nonlinear Neutral Equations
title_full Dynamics of Third-Order Nonlinear Neutral Equations
title_fullStr Dynamics of Third-Order Nonlinear Neutral Equations
title_full_unstemmed Dynamics of Third-Order Nonlinear Neutral Equations
title_short Dynamics of Third-Order Nonlinear Neutral Equations
title_sort dynamics of third order nonlinear neutral equations
url http://dx.doi.org/10.1155/2014/917913
work_keys_str_mv AT huawang dynamicsofthirdordernonlinearneutralequations
AT liliu dynamicsofthirdordernonlinearneutralequations
AT yanxiangtan dynamicsofthirdordernonlinearneutralequations