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Oscillation criteria for second-order nonlinear neutral delay dynamic equations. (English) Zbl 1062.34068
Summary: We establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation $\left(r(t)\left(\left(y(t)+ p(t)y(t-\tau)\right)^\Delta \right)^\gamma\right)^\Delta+f\bigl(t,y(t-\delta)\bigr)=0$ on a time scale $$\mathbb{T}$$; here, $$\gamma >0$$ is a quotient of odd positive integers with $$r(t)$$ and $$p(t)$$ real-valued positive functions defined on $$\mathbb{T}$$. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study.

MSC:
 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations 39A12 Discrete version of topics in analysis
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