Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments

Oscillation criteria for nth order neutral differential equations with deviating arguments of the form (r(t)vertical bar(x(t) + p(t)x(t - iota))((n-1))vertical bar(x-1)(x(t) + p(t)x(t-iota))((n-1)))' + q(t)f(x(sigma(t))) = 0, t >= t(0), it even are established, where p, q is an element of C([t(0), infinity), R), f is an element of C(R, R) and alpha > 0, iota >= 0 are constants. The results obtained essentially improve and extend those of Dzurina and Stavroulakis [J. Dzurina, I.P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comp. 140 (2003) 445-453], Sun and Meng [Y.G. Sun, F.W. Meng, Note on the paper of Dzurina and Stavroulakis, Appl. Math. Comput. 174 (2006) 1634-1641], Xu and Meng [R. Xu, F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 182 (2006) 797-8031. (c) 2007 Elsevier Inc. All rights reserved.