Opuscula Math. 44, no. 5 (2024), 727-748
https://doi.org/10.7494/OpMath.2024.44.5.727
Opuscula Mathematica
Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations
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.
Mathematics Subject Classification: 34C10, 26A24.
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- Kazuki Ishibashi
https://orcid.org/0000-0003-1812-9980- Department of Electrical Systems Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan
- Communicated by Josef Diblík.
- Received: 2024-05-13.
- Revised: 2024-05-31.
- Accepted: 2024-06-01.
- Published online: 2024-07-01.
