## 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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### References:

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