Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations

• Published in: Український математичний журнал
• Date: 2006
• ISSN: 1027-3190
• Main Authors: Yamaoka, N., Sugie, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165546
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations / N. Yamaoka, J. Sugie // Український математичний журнал. — 2006. — Т. 58, № 12. — С. 1704–1714. — Бібліогр.: 15 назв. — англ.

The purpose of this paper is to present new oscillation theorems and nonoscillation theorems for the nonlinear Euler differential equation t²x''′+g(x)=0. Here we assume that xg(x)>0 if x≠0, but we do not necessarily require that g(x) be monotone increasing. The obtained results are best...