Nonlinear oscillation of second order differential equations with state-dependent delays

摘要

Oscillation and nonoscillation criteria are presented for the second order nonlinear differential equation with state-dependent delay(r(t)|y′(t)|p-1y′(t))′+f(t,y(t),y(Δ(t,y(t))))=0in the case ∫∞r-1/p(s)ds<∞. The results established here can be conjugated with the theorems given by Bainov et al. [D.D. Bainov, N.T. Markova, P.S. Simeonov, Asymptotic behavior of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function, J. Comput. Appl. Math. 91 (1998) 87–96] and Luo [J. Luo, Asymptotic behavior of the solutions of second order quasilinear differential equations with delay depending on the unknown function, J. Comput. Appl. Math. 185 (2006) 133–143].