Oscillation criteria for second-order nonlinear delay dynamic equations

In this paper, we consider the second-order nonlinear delay dynamic equation(r(t)xΔ(t)Δ)+p(t)f(x(τ(t)))=0,(r(t)xΔ(t))Δ+p(t)f(x(τ(t)))=0, on a time scale TT. By employing the generalized Riccati technique we will establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. The obtained results improve the well-known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations. Some applications and examples are considered to illustrate the main results.