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Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales. (English) Zbl 1125.34047
The authors establish several new oscillation criteria for second order dynamic equations $$ x^{\Delta\Delta}(t)+p(t)\,x^\gamma(\tau(t))=0 $$ of Emden-Fowler type on an unbounded time scale ${\mathbb T}$ (which is by definition any nonempty closed subset of ${\mathbb R}$). The exponent $\gamma$ is a quotient of odd positive integers, $p(\cdot)$ is positive and rd-continuous, and $\tau:{\mathbb T}\to{\mathbb T}$ is rd-continuous, sublinear, i.e., $\tau(t)\leq t$, and $\tau(t)\to\infty$ as $t\to\infty$. The main tool in deriving these oscillation criteria is a Riccati technique and, in some cases, the Keller--Pötzsche time scale chain rule.

MSC:
34K11Oscillation theory of functional-differential equations
39A10Additive difference equations
39A13Difference equations, scaling ($q$-differences)
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References:
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