Oscillation criteria for second-order neutral equations with distributed deviating argument

We present new oscillation criteria for the second-order neutral delay differential equations with distributed deviating argument(r(t)ψ(x(t))Z′(t))′+∫abp(t,ξ)f[x(g(t,ξ))]dσ(ξ)=0,t⩾t0,where Z(t)=x(t)+q(t)x(t-τ)Z(t)=x(t)+q(t)x(t-τ). New oscillation criteria are established, which are based on a class of new functions Φ(t,s,l)Φ(t,s,l) defined in the sequel. Our results are sharper than some previous results which can be seen by the example at the end of this paper.