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 T, where |f(t,u)|≥q(t)|u^γ|, r, p and q are real valued rd-continuous positive functions defined on T, γ≥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 p^Δ(t)≥0, and ∫_t0^∞θγ(s)q(s)[1-r(θ(s))]^γΔs=∞. Some examples are given to illustrate the main results.