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Oscillation for a class of second-order Emden-Fowler delay dynamic equations on time scales. (English) Zbl 1192.34078
Summary: By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations $$(rx^{\Delta})^{\Delta}(t)+p(t)x^{\gamma }(\tau (t))=0$$ on a time scale $\Bbb T$. Here $\gamma $ is a quotient of odd positive integers with $r$ and $p$ as real-valued positive rd-continuous functions defined on $\Bbb T$. Our results in this paper not only extend the results given in Agarwal et al. (2005), Akin-Bohner et al. (2007) and Han et al. (2007) but also unify the results about oscillation of the second-order Emden-Fowler delay differential equation and the second-order Emden-Fowler delay difference equation.

34K11Oscillation theory of functional-differential equations
34N05Dynamic equations on time scales or measure chains
Full Text: DOI EuDML