Generalized Philos-type oscillation criteria for second order nonlinear neutral delay dynamic equations on time scales

By employing the generalized Riccati transformation w(s)w(s) and showing that [H(σ(t),s)w(s)]Δs≤0[H(σ(t),s)w(s)]Δs≤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.