Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales

Shanliang Zhu and Chunyun Sheng

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-14

Abstract:

We consider the nonlinear dynamic system 𠑥 Δ ( 𠑡 ) = 𠑎 ( 𠑡 ) 𠑔 ( 𠑦 ( 𠑡 ) ) , 𠑦 Δ ( 𠑡 ) = − 𠑓 ( 𠑡 , 𠑥 𠜎 ( 𠑡 ) ) . 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:137471

DOI: 10.1155/2012/137471

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