Oscillation criteria for higher order quasilinear dynamic equations with Laplacians and a deviating argument

In this paper, we deal with the oscillation of the solutions of the higher order quasilinear dynamic equation with Laplacians and a deviating argument in the form of (x[n−1])Δ(t)+p(t)ϕγ(x(g(t)))=0on an above-unbounded time scale, where n ≥ 2, x[i](t):=ri(t)ϕαi[(x[i−1])Δ(t)],i=1,2,…,n−1,withx[0]=x.By using a generalized Riccati transformation and integral averaging technique, we establish some new oscillation criteria for the cases when n is even and odd, and when α > γ, α=γ, and α < γ, respectively, with α=α1⋯αn−1 and without any restrictions on the time scale.