We study the -th-order nonlinear dynamic equations
on an unbounded time scale , where and for
with and ; here the constants and the functions , , are positive and , are nonnegative functions. Criteria are established for the oscillation of solutions for both even- and odd-order cases. The results improve several known results in the literature on second-order, third-order, and higher-order linear and nonlinear dynamic equations. In particular our results can be applied when is not (delta) differentiable and the forward jump operator and do not commute.
"Oscillatory behavior of solutions of dynamic equations of higher order on time scales." Rocky Mountain J. Math. 50 (2) 599 - 617, April 2020. https://doi.org/10.1216/rmj.2020.50.599