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

Saker, S. H.; O’Regan, Donal

Hiroshima Math. J. 42, No. 1, 77-98 (2012).

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.

Reviewer: Zhenlai Han (Jinan)

MSC:

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

Keywords:

oscillation; second-order neutral dynamic equation; time scales

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