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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 Δ ) Δ (t)+p(t)x γ (τ(t))=0

on a time scale 𝕋. Here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on 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.

MSC:
34K11Oscillation theory of functional-differential equations
34N05Dynamic equations on time scales or measure chains
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