Oscillatory Behavior of Noncanonical Quasilinear Second-Order Dynamic Equations on Time Scales

Abstract

The objective of this article is to examine the oscillatory behavior of a class of quasilinear second-order dynamic equations on time scales. Our focus will be on the noncanonical case, which has received relatively less attention compared to the more commonly studied canonical dynamic equations. Our approach involves transforming the noncanonical equation into a corresponding canonical equation. By utilizing this transformation and a range of techniques, we develop new, more efficient, and precise oscillation criteria. Finally, we demonstrate the significance and usefulness of our results by applying them to specific cases within the equation being studied. © 2023 A. Hassan et al.