OSCILLATION OF NONAUTONOMOUS SECOND ORDER NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES

Abstract

In this paper, we establish some new oscillation criteria for nonautonomous second order neutral delay dynamic equation with several delays

$${(x(t)-r(t)x(\tau (t)))}^{△△}+H(t,x(h(t)))+G(t,x(g(t)))=0,$$

on a time scale $\mathbb{T}$. The results not only can be applied on neutral differential equations when $\mathbb{T}=ℝ$, neutral delay difference equations when $\mathbb{T}=\mathbb{N}$ and for neutral delay $q-$ difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for , but also improved most previous results.