时间尺度上具阻尼项的二阶半线性时滞动力方程的振动准则

Oscillation criteria for second-order half-linear delay dynamic equations with damping on time scales

利用广义Riccati变换和不等式技巧,研究了一类具阻尼项的二阶半线性时滞动力方程解的振动性质,在一定条件下,建立了四个新的振动准则,其结果不仅推广和改进了已知的一些结果,而且在时间尺度上统一了具阻尼项的二阶半线性时滞微分方程和差分方程解的振动性质.

By using the generalized Riccati transformation and the inequality technique, we establish four new oscillation criteria for certain second-order half-linear delay dynamic equations with damping on time scales. Our results extend and improve some known results, but also unify the oscillation of the second-order half-linear delay differential equations with damping and the second-order half-linear delay difference equations with damping.