Oscillation Criteria of the Leighton–Wintner‐Type and the Hille–Kneser‐Type for Linear Differential Equations With a Proportional Derivative Controller

ABSTRACT In this study, we investigated the oscillatory and nonoscillatory behavior of solutions to linear differential equations with proportional–derivative (PD) control. In particular, we aimed to extend classical oscillation theorems, such as the Leighton–Wintner oscillation theorem and the Hille–Kneser oscillation and nonoscillation criteria, to make them applicable to this class of equations. The Leighton–Wintner oscillation theorem was proved using the Riccati technique, while the Hille–Kneser oscillation and nonoscillation criteria were derived by clarifying the oscillation constant of Euler‐type equations with PD control.