Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales

This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form [ A ( t ) φ ( y Δ ( t ) ) ] Δ + b ( t ) φ ( y Δ ( t ) ) + P ( t ) F ( φ ( x ( δ ( t ) ) ) ) − Q ( t ) f ( φ ( x ( γ ( t ) ) ) ) = 0 on an arbitrary time scale T , where y ( t ) = x ( t ) + B ( t ) x ( τ ( t ) ) and φ ( u ) = | u | λ − 1 u ( λ > 0 ). By using the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations are established. Our results extend and improve some known results, but they also unify the oscillation of second-order Emden-Fowler delay differential equations with damping and second-order Emden-Fowler delay difference equations with damping. Examples are given to illustrate the importance of our results.