language 
eng

Author 
Ishibashi, Kazuki
Department of Electronic Control Engineering, National institute of Technology, Hiroshima College,

Description  As is well known, Mathieu’s equation is a representative of mathematical models describing
parametric excitation phenomena. This paper deals with the oscillation problem for Mathieu’s equation with two frequencies. The ratio of these two frequencies is not necessarily a rational number. When the ratio is an irrational number, the coefficient of Mathieu’s equation is is quasiperiodic, but not periodic. For this reason, the basic knowledge for linear periodic systems such as Floquet theory is not useful. Whether all solutions of Mathieu’s equation oscillate or not is determined by parameters and frequencies. Our results provide parametric conditions to guarantee that all solutions are nonoscillatory. The advantage of the obtained parametric conditions is that it can be easily checked. Parametric nonoscillation region is drawn to understand these results easily. Finally, several simulations are carried out to clarify the remaining problems. 
Subject  Nonoscillation
Parametric excitation
Mathieu’s equation
Frequencies
Quasiperiodic

Journal Title 
Applied Mathematics and Computation

Volume  346

Start Page  491

End Page  499

ISSN  00963003

Published Date  201904

DOI  
Publisher  Elsevier

NII Type 
Journal Article

Format 
PDF

Text Version 
著者版

OAIPMH Set 
Department of Mathematics, Faculty of Science and Engineering
