Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales

This paper establishes new Kneser-type oscillation criteria for a class of third-order half-linear dynamic equations on time scales. The analysis is based on a Riccati-type transformation, which reduces the original equation to an associated dynamic inequality and yields explicit oscillation conditions. The obtained criteria extend existing results from second-order to third-order equations and provide a unified treatment of continuous and discrete cases. To the best of our knowledge, no comparable Kneser-type oscillation criteria have been reported for equations of the form considered here. Several examples illustrate the applicability of the main results.