@Article{Ishibashi2024,
author = "Ishibashi, Kazuki",
title = "Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "5",
pages = "727--748",
doi = "https://doi.org/10.7494/OpMath.2024.44.5.727",
url = "https://doi.org/10.7494/OpMath.2024.44.5.727",
abstract = "In this study, we addressed the nonoscillation of th 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.",
keywords = "nonoscillation, conformable differential equation, proportional-derivative controller, Riccati technique, Euler equation",
issn = "1232-9274"
}