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 formr(t)|(x(t)+p(t)x(t-τ))(n-1)|α-1(x(t)+p(t)x(t-τ))(n-1)′+q(t)f(x(σ(t)))=0,t⩾t0,n   even are established, where p,q∈C([t0,∞),R),f∈C(R,R)p,q∈C([t0,∞),R),f∈C(R,R) and α>0α>0, τ⩾0τ⩾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) 797–803].