时间尺度上二阶Emden-Fowler型延迟动态方程的振动性

Oscillation for a class of second-order Emden-Fowler-type delay dynamic equations on time scales

研究了时间尺度上一类二阶非线性中立型阻尼Emden-Fowler型延迟泛函动态方程的振动性,利用时间尺度上的微积分理论和广义的Riccati变换、Yang不等式、H9lder不等式以及一些分析技巧,在两种情形下建立了该方程的几个新的振动准则,所得结果充分反映了阻尼项和中立项在系统振动中的影响作用,所举例子说明,这些准则不仅推广并改进了一些已有的结果,而且具有较好的实用性和可操作性.

We studied the oscillatory behavior of a certain class of second-order nonlinear neutral damped Emden-Fowler-type delay functional dynamic equations on time scales.By using the calculus theory on time scales and the generalized Riccati transformation,Yang’s inequality,H lder’s inequality and mathematical analytic methods,we established some new oscillation criteria for the equations in two cases.The results fully reflect the influential actions of damping terms and neutral terms in system oscillation.The illustrative examples show that our results extend and improve those reported in the literature and that they have practicability and maneuverability.