Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
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...
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| Date: | 2006 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2006
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/165546 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 possible in a certain sense. To establish our results, we use Sturm’s comparison theorem for linear Euler differential equations and phase plane analysis for a nonlinear system of Liénard type. |
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