Generalized Philos-type oscillation criteria for second order nonlinear neutral delay dynamic equations on time scales. (English) Zbl 1335.34143
Summary: By employing the generalized Riccati transformation \(w(s)\) and showing that \([H(\sigma(t), s) w(s)]^{\Delta_s} \leq 0\), we establish new Philos-type oscillation criteria for second order nonlinear dynamic equations on time scales. The obtained results essentially generalize and improve the well-known oscillation results for half-linear dynamic equations such as Philos-type and Kamenev-type oscillation criteria. We illustrate the versatility of our results by means of examples.
MSC:
| 34N05 | Dynamic equations on time scales or measure chains |
| 34K11 | Oscillation theory of functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K17 | Transformation and reduction of functional-differential equations and systems, normal forms |
Keywords:
second order nonlinear neutral delay dynamic equations; Philos-type oscillation criteria; generalized Riccati transformationReferences:
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