时间测度链上一类具阻尼项的二阶动力方程的振动准则

Oscillation Criteria for a Class of Second Order Dynamic Equations with Damping on Time Scales

研究了时间测度链上一类具有阻尼项和非线性中立项的二阶非线性变时滞动力方程的振动性,利用时间测度链上的理论,结合广义的Riccati变换和一些不等式技巧,得到了该方程的几个新的振动准则.这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了具有阻尼项的二阶非线性时滞微分方程和差分方程的振动性质.最后,举例说明文中给出的主要结论.

The oscillation for certain second-order nonlinear variable delay dynamic equations with damping term and nonlinear neutral term on time scales was discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations were established. The results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations and second-order nonlinear delay difference equations with damping term. Some examples were given to illustrate the main results of this article.