Some New Oscillation Criteria for Higher–order Quasi–linear Neutral Delay Differential Equations

Oscillation criteria for the higher order quasi-linear neutral delay differential equations of the form [r(t)ψ(u(t))|z(n−1)(t)|α−1z(n−1)(t)]′ + m ∑ i=1 qi(t) fi(|u(τi(t))|αi−1u(τi(t))) = 0, t t0, z(t) = u(t) + p(t)u(t −σ),α > 0,αi > 0 (i = 1,2,3, ...,m) , are established under the condition: ∫ ∞ t0 r− 1 α (s)ds = ∞ or ∫ ∞ t0 r− 1 α (s)ds < ∞ respectively, where n is even. The obtained results improve and extend some known results in literature.