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

Abstract Oscillation criteria for nth order neutral differential equations with deviating arguments of the form r ( 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 ⩾ t 0 , n even are established, where p , q ∈ C ( [ t 0 , ∞ ) , R ) , f ∈ C ( R , R ) and α > 0 , τ ⩾ 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].