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Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. (English) Zbl 1246.34066

The paper considers the second order dynamic equation on time scale \(\mathbb{T}\) \[ x^{\Delta\Delta}(t)+p(t)f(x(\sigma(t)))=0, \] where \(p\in C(\mathbb{T},\mathbb{R}), \) \(f:\mathbb{R}\to \mathbb{R}\) is a continuously differentiable function with superlinearity such that \(f'(x)>0\), \(xf(x)>0\) for \(x\not=0\). Two sufficient conditions for the equation to be oscillatory are given.

MSC:

34K11 Oscillation theory of functional-differential equations
34N05 Dynamic equations on time scales or measure chains
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