TY  - JOUR
ID  - Ishibashi2024
LB  - Ishibashi2024
AU  - Ishibashi, Kazuki
TI  - Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations
ST  - Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 727
EP  - 748
DO  - https://doi.org/10.7494/OpMath.2024.44.5.727
UR  - https://doi.org/10.7494/OpMath.2024.44.5.727
AB  - 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.
KW  - nonoscillation
KW  - conformable differential equation
KW  - proportional-derivative controller
KW  - Riccati technique
KW  - Euler equation
SN  - 1232-9274
ER  -