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

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
Main Authors: Yamaoka, N., Sugie, J.
Format: Article
Language:English
Published: Інститут математики НАН України 2006
Series:Український математичний журнал
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Online Access:https://nasplib.isofts.kiev.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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spelling nasplib_isofts_kiev_ua-123456789-1655462025-02-09T11:00:42Z Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations Багатошарові структури лінійних диференціальних рівнянь другого порядку типу Ейлера та їх застосування до нелінійних коливань Yamaoka, N. Sugie, J. Статті 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. Наведено нові осцнляційні та неосцнляційні теореми для нелінійного диференціального рівняння Ейлера t²x''′+g(x)=0, де припускається, що xg(x)>0 при x≠0, але вимога про монотонне зростання g(x) не є обов'язковою. Одержані результати є найкращими у певному сенсі. Для їх встановлення використано порівняльну теорему Штурма для лінійних диференціальних рівнянь Ейлера та фазовий площинний аналіз для нелінійної системи типу Льєнарда. Supported in part by Grant-in-Aid for Scientific Research 16540152 2006 Article 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. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/165546 517.9 en Український математичний журнал application/pdf Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Статті
Статті
spellingShingle Статті
Статті
Yamaoka, N.
Sugie, J.
Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
Український математичний журнал
description 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.
format Article
author Yamaoka, N.
Sugie, J.
author_facet Yamaoka, N.
Sugie, J.
author_sort Yamaoka, N.
title Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
title_short Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
title_full Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
title_fullStr Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
title_full_unstemmed Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations
title_sort multilayer structures of second-order linear differential equations of euler type and their application to nonlinear oscillations
publisher Інститут математики НАН України
publishDate 2006
topic_facet Статті
url https://nasplib.isofts.kiev.ua/handle/123456789/165546
citation_txt 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.
series Український математичний журнал
work_keys_str_mv AT yamaokan multilayerstructuresofsecondorderlineardifferentialequationsofeulertypeandtheirapplicationtononlinearoscillations
AT sugiej multilayerstructuresofsecondorderlineardifferentialequationsofeulertypeandtheirapplicationtononlinearoscillations
AT yamaokan bagatošarovístrukturilíníjnihdiferencíalʹnihrívnânʹdrugogoporâdkutipuejlerataíhzastosuvannâdonelíníjnihkolivanʹ
AT sugiej bagatošarovístrukturilíníjnihdiferencíalʹnihrívnânʹdrugogoporâdkutipuejlerataíhzastosuvannâdonelíníjnihkolivanʹ
first_indexed 2025-11-25T20:56:26Z
last_indexed 2025-11-25T20:56:26Z
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