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

In this paper, some new oscillation criteria for second order neutral nonlinear differential equation[r(t)|(x(t)+p(t)x((σ(t))))′|m-1(x(t)+p(t)x((σ(t))))′]′+q(t)f(x(τ(t)))=0[r(t)|(x(t)+p(t)x((σ(t))))′|m-1(x(t)+p(t)x((σ(t))))′]′+q(t)f(x(τ(t)))=0are established. New oscillation criteria are different from most known ones in the sense that they are based on a class of new functions Φ(t,s,l)Φ(t,s,l) defined in the sequel.