Oscillation and nonoscillation criteria for linear dynamic systems on time scales.(English)Zbl 1193.34181

Summary: We establish oscillation and nonoscillation criteria for the linear dynamic system $$u^{\Delta}=pv$$, $$v^{\Delta}=-qu^{\sigma}$$. Here we assume that $$p$$ and $$q$$ are nonnegative, rd-continuous functions on a time scale $$\mathbb{T}$$ such that $$\sup\mathbb{T}=\infty$$. Indeed, we extend some known oscillation results for differential systems and difference systems to the so-called dynamic systems.

MSC:

 34N05 Dynamic equations on time scales or measure chains 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:

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