Leighton–Wintner‐Type Oscillation Criteria for the p(t)‐Laplacian Dynamic Equations on Time Scales

ABSTRACT This study investigates oscillation problems for ‐Laplacian dynamic equations on time scales. By employing the Riccati transformation technique, we establish a new Leighton–Wintner‐type oscillation theorem for the equations under consideration, which unifies and extends existing results for both differential and difference equations. As illustrative examples, we present several equations, including differential equations on , difference equations on , equations on hybrid time scales combining continuous and discrete parts, and ‐difference equations, and show that all proper solutions are oscillatory. The effectiveness of the obtained results is confirmed through numerical simulations.