Oscillation for second-order half-linear delay damped dynamic equations on time scales

We investigate oscillation of second-order half-linear variable delay damped dynamic equations a(t) x (t) .-1 x (t) + b(t) x (t) .-1 x (t) + p(t) x(d(t)) .-1 x(d(t)) = 0 on a time scale T. By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the equations under the condition 8 t0 a-1(s) e-b/a(s, t0) 1/. s <8. These results deal with some cases not covered by existing results in the literature.