Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales
We consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale 𝕋 and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/747838 |
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| _version_ | 1832554287889121280 |
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| author | Xinli Zhang Shanliang Zhu |
| author_facet | Xinli Zhang Shanliang Zhu |
| author_sort | Xinli Zhang |
| collection | DOAJ |
| description | We consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale 𝕋 and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case where b(t)≠0 for all t∈𝕋 and g(u)=u. Some examples are given to illustrate the results. |
| format | Article |
| id | doaj-art-667490db15da400ab97b999245eb1ecb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-667490db15da400ab97b999245eb1ecb2025-02-03T05:51:57ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/747838747838Oscillation for a Nonlinear Dynamic System with a Forced Term on Time ScalesXinli Zhang0Shanliang Zhu1College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaCollege of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaWe consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale 𝕋 and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case where b(t)≠0 for all t∈𝕋 and g(u)=u. Some examples are given to illustrate the results.http://dx.doi.org/10.1155/2014/747838 |
| spellingShingle | Xinli Zhang Shanliang Zhu Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales Abstract and Applied Analysis |
| title | Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales |
| title_full | Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales |
| title_fullStr | Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales |
| title_full_unstemmed | Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales |
| title_short | Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales |
| title_sort | oscillation for a nonlinear dynamic system with a forced term on time scales |
| url | http://dx.doi.org/10.1155/2014/747838 |
| work_keys_str_mv | AT xinlizhang oscillationforanonlineardynamicsystemwithaforcedtermontimescales AT shanliangzhu oscillationforanonlineardynamicsystemwithaforcedtermontimescales |