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.
Reviewer: Fozi Dannan (Damascus)
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 |
Keywords:
time scales; oscillation; variable delay; second order nonlinear neutral dynamic equations; generalized Riccati technique; integral averaging techniqueReferences:
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