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)vertical bar (x(t) + P(t)x(t- tau))'vertical bar(alpha-1) (x(t) + p(t)x(t -tau))']' + q(t)f(x(t-sigma))g(x'(t))=0, where t >= t(0), alpha > 0, tau >= 0, and sigma >= 0 are constants, a, q is an element of C ([t(0), infinity)); R), p is an element of C-1( [t(0), infinity); R), f, g is an element of C (R; R), are studied. Our results generalize and improve some known results of neutral delay differential equations. (C) 2006 Elsevier Ltd. All rights reserved.