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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |