Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales - Shanliang Zhu; Chunyun Sheng (Discrete Dynamics in Nature and Society)
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.