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Oscillation criteria for half-linear dynamic equations on time scales. (English) Zbl 1156.34022
The author considers the second-order half-linear dynamic equation
\[ (r(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+p(t)x^{\gamma}(t)=0\tag{1} \] on an arbitrary time scale \(\mathbb{T}\) (\(\sup\mathbb T=\infty\)), where \(\gamma\) is the quotient of odd positive integers, \(r(t)\) and \(p(t)\) are positive rd-continuous functions on \(\mathbb{T}\). Main results of the paper are sufficient conditions for every solution of (1) to be oscillatory. As the author remarks, when \(\mathbb T=\mathbb R\), the obtained results improve several results known for differential equations and when \(\mathbb T=\mathbb N\), then they improve some results known for second order difference equations.

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
39A10 Additive difference equations
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