Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker–Hill-type equation

The nonoscillation of Mathieu-type half-linear differential equations was investigated. The particular equation under consideration is an extension of the Mathieu equation, which has been widely applied in mechanical and electrical engineering. The investigation led to the main finding that all nont...

Full description

Saved in:
Bibliographic Details
Published inMonatshefte für Mathematik Vol. 198; no. 4; pp. 741 - 756
Main Author Ishibashi, Kazuki
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.08.2022
Springer Nature B.V
Subjects
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Theorems
Nonoscillation
34C10
Half-linear differential equation
Mathieu’s equation
34B30
Riccati technique
Comparison theorem
Whittaker–Hill’s equation
Online AccessGet full text

Cover

More Information
Summary:The nonoscillation of Mathieu-type half-linear differential equations was investigated. The particular equation under consideration is an extension of the Mathieu equation, which has been widely applied in mechanical and electrical engineering. The investigation led to the main finding that all nontrivial solutions of the Mathieu-type half-linear differential equations are nonoscillatory under simple parametric conditions. Proving the finding requires a simple nonoscillation theorem to compare the two equations. As another application of the findings, by using a simple nonoscillation comparison theorem, we propose that all nontrivial solutions of the half-linear Whittaker–Hill-type equation do not oscillate.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-022-01720-2