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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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