New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution

In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation(p(t)([y(t)+r(t)y(τ(t))]Δ)γ)Δ+f(t,y(θ(t))=0,t∈[t0,∞)T,on a time scale TT, where |f(t,u)|⩾q(t)|uγ||f(t,u)|⩾q(t)|uγ|, r, p and q are real valued rd  -continuous positive functions defined on TT, γ⩾1γ⩾1 is the quotient of odd positive integers. Our results improve existence results in the literature in the sense that our results do not require pΔ(t)⩾0pΔ(t)⩾0, and ∫t0∞θγ(s)q(s)[1-r(θ(s))]γΔs=∞. Some examples are given to illustrate the main results.