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Oscillation criteria for half-linear dynamic equations on time scales. (English) Zbl 1156.34022

The author considers the second-order half-linear dynamic equation

(r(t)(x Δ (t)) γ ) Δ +p(t)x γ (t)=0(1)

on an arbitrary time scale 𝕋 (sup𝕋=), where γ is the quotient of odd positive integers, r(t) and p(t) are positive rd-continuous functions on 𝕋. Main results of the paper are sufficient conditions for every solution of (1) to be oscillatory. As the author remarks, when 𝕋=, the obtained results improve several results known for differential equations and when 𝕋=, then they improve some results known for second order difference equations.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
39A10Additive difference equations
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