We establish some oscillation criteria for the third-order Emden–Fowler neutral delay dynamic equations of the form: (a(t)(x(t)+r(t)x(τ(t)))ΔΔ)Δ+p(t)xγ(δ(t))=0\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} (a(t)(x(t)+r(t)x(\tau (t)))^{\Delta \Delta })^\Delta +p(t)x^\gamma (\delta (t))=0 \end{aligned}$$\end{document}on a time scale T\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {T}$$\end{document}, where γ>0\documentclass[12pt]{minimal}
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\begin{document}$$\gamma >0$$\end{document} is a quotient of odd positive integers, and a and p are real-valued positive rd-continuous functions defined on T\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {T}$$\end{document}. Due to the different values of γ\documentclass[12pt]{minimal}
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\begin{document}$$\gamma $$\end{document}, we give not only the oscillation criteria for superlinear neutral delay dynamic equations, but also the oscillation criteria for sublinear neutral delay dynamic equations based on the Hille and Nehari-type oscillation criteria. Our results extend and improve some known results in the literature and are new even for the corresponding third-order differential equations and difference equations as our special cases.
