Oscillation criteria of second-order quasi-linear neutral delay differential equations

The oscillatory and non-oscillatory behavior of solutions of the second-order quasi-linear neutral delay differential equation [a(t)|(x(t)+p(t)x(t−τ))′|α−1(x(t)+p(t)x(t−τ))′]′+q(t)f(x(t−σ))g(x′(t))=0,[a(t)|(x(t)+p(t)x(t−τ))′|α−1(x(t)+p(t)x(t−τ))′]′+q(t)f(x(t−σ))g(x′(t))=0, where t≥t0,α>0,τ≥0t≥t0,α>0,τ≥0, and σ≥0σ≥0 are constants, a,q∈C([t0,∞);R),p∈C1([t0,∞);R),f,g∈C(R;R)a,q∈C([t0,∞);R),p∈C1([t0,∞);R),f,g∈C(R;R), are studied. Our results generalize and improve some known results of neutral delay differential equations.