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Oscillation criteria for second order linear equations on a time scale. (English) Zbl 1050.39024

Summary: We apply averaging techniques to develop oscillation criteria for the second order scalar differential equation \((r(t) x^\Delta(t))^\Delta+ q(t) x^\sigma(t)=0\), on a time scale (measure chain) \(\mathbb{T}\). These results extend some earlier criteria for the differential and difference equation case.

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34B24 Sturm-Liouville theory
39A11 Stability of difference equations (MSC2000)
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