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Oscillation criteria for second-order nonlinear neutral variable delay dynamic equations. (English) Zbl 1104.39009

Authors’ abstract: This paper is concerned with oscillation of second order nonlinear neutral dynamic equations on time scales with a variable delay. By using the generalized Riccati technique and integral averaging technique, new oscillation criteria are obtained for all solution of the equation. Some results extend known results for difference equations when the time scale is the set \({\mathbb Z}^{+}\) of positive integers and for differential equations when the time scale is \({\mathbb R}\). Several examples are given to illustrate the results of the paper.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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