Determination of the boundaries between the domains of stability and instability for the Hill's equation

• Published in: Нелінійні коливання
• Date: 2003
• Main Authors: Grebenikov, E.A., Prokopenya, A.N.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/176161
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Determination of the boundaries between the domains of stability and instability for the Hill's equation / E.A. Grebenikov, A.N. Prokopenya // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 42-51. — Бібліогр.: 12 назв. — англ.

Stability problem for the Hill’s equation containing two parameters is analyzed with computer algebra system M athematica. The characteristic constant is found as a series expansion in powers of a small parameter e. It has been shown that the domains of instability are located only between the c...