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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 ΔΔ (t)+p(t)x γ (τ(t))=0

of Emden-Fowler type on an unbounded time scale 𝕋 (which is by definition any nonempty closed subset of ). The exponent γ is a quotient of odd positive integers, p(·) is positive and rd-continuous, and τ:𝕋𝕋 is rd-continuous, sublinear, i.e., τ(t)t, and τ(t) as t. The main tool in deriving these oscillation criteria is a Riccati technique and, in some cases, the Keller–Pötzsche time scale chain rule.

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