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Zbl 1156.34022
Hassan, Taher S.
Oscillation criteria for half-linear dynamic equations on time scales.
(English)
[J] J. Math. Anal. Appl. 345, No. 1, 176-185 (2008). ISSN 0022-247X

The author considers the second-order half-linear dynamic equation $$(r(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+p(t)x^{\gamma}(t)=0\tag1$$ on an arbitrary time scale $\Bbb{T}$ ($\sup\Bbb T=\infty$), where $\gamma$ is the quotient of odd positive integers, $r(t)$ and $p(t)$ are positive rd-continuous functions on $\Bbb{T}$. Main results of the paper are sufficient conditions for every solution of (1) to be oscillatory. As the author remarks, when $\Bbb T=\Bbb R$, the obtained results improve several results known for differential equations and when $\Bbb T=\Bbb N$, then they improve some results known for second order difference equations.
[Jan Ohriska (Košice)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
39A10 Difference equations

Keywords: oscillation theory; half-linear dynamic equations; time scales

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