Some new oscillation criteria for second order quasi-linear neutral delay differential equations

摘要

In this paper, we will establish some new oscillation criteria for second order quasi-linear neutral delay differential equations of the form[r(t)|(x(t)+p(t)x(t-τ))′|α-1(x(t)+p(t)x(t-τ))′]′+q(t)f(x(σ(t)))=0.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. Comput. 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].