Improved Hille-Type and Ohriska-Type Criteria for Half-Linear Third-Order Dynamic Equations

In this paper, we examine the oscillatory behavior of solutions to a class of half-linear third-order dynamic equations with deviating arguments {(2) ()(2) ([(1) ()(1) ((Delta) ())](Delta))}(Delta) + () ((())) = 0, on an arbitrary unbounded-above time scale T, where is an element of [(0), infinity) := [(0), infinity) boolean AND , (0) >= 0, (0) is an element of T and () := || sgn, zeta > 0. Using the integral mean approach and the known Riccati transform methodology, several improved Hille-type and Ohriska-type oscillation criteria have been derived that do not require some restrictive assumptions in the relevant results. Illustrative examples and conclusions show that these criteria are sharp for all third-order dynamic equations compared to the previous results in the literature.