## New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution.(English)Zbl 1252.34104

The authors consider the second-order nonlinear neutral functional dynamic equation $(p(t)([y(t)+r(t)y(\tau(t))]^{\Delta})^{\gamma})^{\Delta}+f(t,y(\delta(t)))=0$ on a time-scale $$T$$ and establish some new sufficient conditions for oscillation. This type of equation has not been studied yet, so the main results in this paper are new. Also, the obtained results cover the cases when $$\delta(T)>t$$ and when $$\delta(T)\leq t$$. The results in this paper can be applied to any time-scale.

### MSC:

 34N05 Dynamic equations on time scales or measure chains 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations
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### References:

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