In this paper, we establish the existence of nonoscillatory solutions to third-order nonlinear neutral dynamic equations on time scales of the form (r1(t)(r2(t)(x(t)+p(t)x(g(t)))Δ)Δ)Δ+f(t,x(h(t)))=0 by employing Kranoselskii’s fixed point theorem. Three examples are included to illustrate the significance of the conclusions.

We establish several oscillation criteria for a class of third-order nonlinear dynamic equations with a damping term and a nonpositive neutral coefficient by using the Riccati transformation. Two illustrative examples are presented to show the significance of the results obtained.

In this paper, we establish oscillation criteria of third-order nonlinear dynamic equations with nonpositive neutral coefficients on time scales by a generalized Riccati transformation and employing functions in some function classes. Two examples are presented to show the significance of the results.

Using functions from some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))k∘xΔ(t))Δ+f(t,x(σ(t)))=0. Two examples are included to show the significance of the results.