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

作者：Xu; Zhiting

来源：Applied Mathematics and Computation, 2008, 206(1): 198-204.

DOI：10.1016/j.amc.2008.09.004

• Oscillation
• Nonoscillation
• Nonlinear
• Second order differential equations
• State-dependent delays

Oscillation and nonoscillation criteria are presented for the second order nonlinear differential equation with state-dependent delay
(r(t)vertical bar y'(t)vertical bar(p-1)y'(t))' f(t, y(t), y(Delta(t, y(t)))) = 0
in the case integral(infinity) r(-1/p) (S) ds < infinity. 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].

• 出版日期2008-12-1
• 单位华南师范大学