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)psi(x(t))Z'(t))' + integral(b)(a) p(t, xi)f[x(g(t,xi))]d sigma(xi) = 0, t >= t(0), where Z(t) = x(t) + q(t)x(t - tau). New oscillation criteria are established, which are based on a class of new functions Phi(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. (c) 2008 Elsevier Inc. All rights reserved.