Oscillation of second-order delay differential equations with mixed nonlinearities

摘要

In this paper, we study the following second-order delay differential equation with mixed nonlinearities(r(t)|u′(t)|α-1u′(t))′+q0(t)|u[τ0(t)]|α-1u[τ0(t)]+q1(t)|u[τ1(t)]|β-1u[τ1(t)]+q2(t)|u[τ2(t)]|γ-1u[τ2(t)]=0,where γ>α>β>0. Oscillation criteria for the equation are established which generalize the results by Džurina and Stavroulakis [J.D. Džurina, I.P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140 (2003) 44–453] and by Sun and Meng [Y.G. Sun, F.W. Meng, Note on the paper of Džurina and Stavroulakis, Appl. Math. Comput. 174 (2006) 1634–1641].