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

摘要

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 $$igl[A(t)arphiigl(y^{Delta} (t)igr)igr]^{Delta} + b(t) arphiigl(y^{Delta} (t)igr) + P(t)Figl(arphiigl(xigl(delta(t) igr)igr)igr) - Q(t)figl(arphiigl(xigl(gamma(t)igr)igr)igr) = 0 $$ on an arbitrary time scale T, where y ( t ) = x ( t ) + B ( t ) x ( τ ( t ) ) $y(t) = x(t) + B(t)x(au (t))$ and φ ( u ) =