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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/917913 |
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| _version_ | 1849686127280128000 |
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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. |
| format | Article |
| id | doaj-art-b8ca7ecb49c541cd8b7425f67e372b9c |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| 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 |