In this paper, we establish the existence of nonoscillatory solutions to third-order nonlinear neutral dynamic equations on time scales of the form (r 1 (t)(r 2 (t)( x(h(t))) = 0 by employing Kranoselskii's fixed point theorem. Three examples are included to illustrate the significance of the conclusions.

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We study the existence of nonoscillatory solutions to a class of third-order neutral functional dynamic equations on time scales. The integral convergence and divergence of the reciprocal of the coefficients in the equations are different. Two examples are given to demonstrate the results.

By employing Krasnoselskii's fixed point theorem, we establish the existence of nonoscillatory solutions to a class of thirdorder neutral functional dynamic equations on time scales. In addition, the significance of the results is illustrated by three examples.

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.