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Oscillation criteria for a generalized Emden-Fowler dynamic equation on time scales. (English) Zbl 1419.34177

Summary: In this paper, we consider the second-order Emden-Fowler neutral delay dynamic equation \[ (r(t)|z^{\Delta}(t)|^{\alpha-1}z^{\Delta}(t))^{\Delta}+q(t)|x(\delta(t))|^{\beta-1}x(\delta(t))=0, \] on time scales, where \(z(t)=x(t)+p(t)x (\tau(t))\) and \(\beta\geq\alpha>0\) are constants. By means of the Riccati transformation and inequality technique, some oscillation criteria are established, which extend and improve some known results in the literature.

MSC:

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

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