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Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations

Ishibashi Kazuki

Opuscula Mathematica

2024

Vol. 44, no. 5

727--748

In this study, we addressed the nonoscillation of the Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type nonoscillation theorem was established to be applied to such equations. Using this theorem, we provided a sharp nonoscillation condition that guarantees that all nontrivial solutions to Euler-type conformable linear equations do not oscillate. The main nonoscillation theorems can be proven by introducing a Riccati inequality, which corresponds to the conformable linear equation of the Sturm-Liouville type.