Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales
We consider the nonlinear dynamic system 𝑥Δ(𝑡)=𝑎(𝑡)𝑔(𝑦(𝑡)),𝑦Δ(𝑡)=−𝑓(𝑡,𝑥𝜎(𝑡)). We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/137471 |
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| _version_ | 1832563252126547968 |
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| author | Shanliang Zhu Chunyun Sheng |
| author_facet | Shanliang Zhu Chunyun Sheng |
| author_sort | Shanliang Zhu |
| collection | DOAJ |
| description | We consider the nonlinear dynamic system 𝑥Δ(𝑡)=𝑎(𝑡)𝑔(𝑦(𝑡)),𝑦Δ(𝑡)=−𝑓(𝑡,𝑥𝜎(𝑡)). We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results. |
| format | Article |
| id | doaj-art-e29f68ae9cea4a48a6fdf0db6f50f1ad |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e29f68ae9cea4a48a6fdf0db6f50f1ad2025-02-03T01:20:37ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/137471137471Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time ScalesShanliang Zhu0Chunyun Sheng1College 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 the nonlinear dynamic system 𝑥Δ(𝑡)=𝑎(𝑡)𝑔(𝑦(𝑡)),𝑦Δ(𝑡)=−𝑓(𝑡,𝑥𝜎(𝑡)). We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.http://dx.doi.org/10.1155/2012/137471 |
| spellingShingle | Shanliang Zhu Chunyun Sheng Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales Discrete Dynamics in Nature and Society |
| title | Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales |
| title_full | Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales |
| title_fullStr | Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales |
| title_full_unstemmed | Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales |
| title_short | Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales |
| title_sort | oscillation and nonoscillation criteria for nonlinear dynamic systems on time scales |
| url | http://dx.doi.org/10.1155/2012/137471 |
| work_keys_str_mv | AT shanliangzhu oscillationandnonoscillationcriteriafornonlineardynamicsystemsontimescales AT chunyunsheng oscillationandnonoscillationcriteriafornonlineardynamicsystemsontimescales |