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Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.

Oscillation criteria for second-order nonlinear neutral delay dynamic equations. (English) Zbl 1062.34068

J. Math. Anal. Appl. 300, No. 1, 203-217 (2004).
Summary: We establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation \[ \left(r(t)\left(\left(y(t)+ p(t)y(t-\tau)\right)^\Delta \right)^\gamma\right)^\Delta+f\bigl(t,y(t-\delta)\bigr)=0 \] on a time scale \(\mathbb{T}\); here, \(\gamma >0\) is a quotient of odd positive integers with \(r(t)\) and \(p(t)\) real-valued positive functions defined on \(\mathbb{T}\). To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study.

Cited in 81 Documents

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
39A12 Discrete version of topics in analysis

Keywords:

Oscillation; Neutral; Delay; Dynamic equations; Time scale
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\textit{R. P. Agarwal} et al., J. Math. Anal. Appl. 300, No. 1, 203--217 (2004; Zbl 1062.34068)
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