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 t ) ( [ y ( t ) + r ( t ) y ( τ ( t ) ) ] Δ ) γ ) Δ + f ( t , y ( θ ( t ) ) = 0 , t ∈ [ t 0 , ∞ ) 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 ∫ t 0 ∞ θ γ ( s ) q ( s ) [ 1 - r ( θ ( s ) ) ] γ Δ s = ∞ . Some examples are given to illustrate the main results.