Oscillation criteria for second order quasilinear neutral delay differential equations on time scales

In this paper, we consider the second-order quasilinear neutral dynamic equation (r(t)|ZΔ(t)|α−1ZΔ(t))Δ+q(t)|x(δ(t))|β−1x(δ(t))=0,(r(t)|ZΔ(t)|α−1ZΔ(t))Δ+q(t)|x(δ(t))|β−1x(δ(t))=0, on a time scale TT, where Z(t)=x(t)+p(t)x(τ(t))Z(t)=x(t)+p(t)x(τ(t)), αα, β>0β>0 are constants, and obtain oscillation criteria for the equation when β>αβ>α, β=αβ=α and β<αβ<α, respectively. Our results extend some known results when p(t)=0p(t)=0 in the literature and contain the continuous and discrete cases as special cases.