Oscillatory And Nonoscillatory Criteria For Several Classes Of Dynamic Equations On Time Scales

In this paper, by making use of the supplementary function as the same as the reference [1], we establish the sufficient condition for the existence of nonoscillatory solution of the second order nonlinear dynamic equationWe also discuss the oscillation and the existence of nonoscillatory solution of the second order half-linear dynamic equationwhereβ>α> 0, q(t)≥0 and q(t)∈C_rd(T).Next, by using Taylor's formula, we study the asymptotic and oscillatory behavior of the high order neutral dynamic equation with variable coefficients,where p (t),q(t)∈C_rd(T), p (t) is bounded, p (t)≥-1 or p (t)≤-1, q(t)≥q>0;σ,τ∈T,σ>0,τ>0, and n is a positive integer. We obtain a series of sufficient conditions for oscillation of above equations.