Second-Order Dynamic Equations with Noncanonical Operator: Oscillatory Behavior

Abstract

The present article aims to study the oscillatory properties of a class of second-order dynamic equations on time scales. We consider during this study the noncanonical case, which did not receive much attention compared to the canonical dynamic equations. The approach adopted depends on converting the noncanonical equation to a corresponding canonical equation. By using this transformation and based on several techniques, we create new, more effective, and sharp oscillation criteria. Finally, we explain the effectiveness and importance of the results by applying them to some special cases of the studied equation.