Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n
In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1<n\in\mathbb{N}$, we obtain conditions for their blow-up in finite time, and some properties for global solutions. Equations containing more general nonlinear terms are...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-11-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/250/abstr.html |
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doaj-1486f0ff4f354d139058abc4587440dd2020-11-24T21:02:00ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-11-012013250,110Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^nMeng-Rong Li0Hsin-Yu Yao1Yu-Tso Li2 National Chengchi Univ., Taipei, Taiwan National Chengchi Univ., Taipei, Taiwan Feng Chia Univ., Taichung, Taiwan In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1<n\in\mathbb{N}$, we obtain conditions for their blow-up in finite time, and some properties for global solutions. Equations containing more general nonlinear terms are also considered.http://ejde.math.txstate.edu/Volumes/2013/250/abstr.htmlNonlinear differential equationEmden-Fowler equationblow-up rate |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Meng-Rong Li Hsin-Yu Yao Yu-Tso Li |
| spellingShingle |
Meng-Rong Li Hsin-Yu Yao Yu-Tso Li Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n Electronic Journal of Differential Equations Nonlinear differential equation Emden-Fowler equation blow-up rate |
| author_facet |
Meng-Rong Li Hsin-Yu Yao Yu-Tso Li |
| author_sort |
Meng-Rong Li |
| title |
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| title_short |
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| title_full |
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| title_fullStr |
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| title_full_unstemmed |
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| title_sort |
asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2013-11-01 |
| description |
In this article we study properties of positive solutions
of the ordinary differential equation $t^2u''=u^n$ for
$1<n\in\mathbb{N}$, we obtain conditions for their blow-up
in finite time, and some properties for global solutions.
Equations containing more general nonlinear terms are also considered. |
| topic |
Nonlinear differential equation Emden-Fowler equation blow-up rate |
| url |
http://ejde.math.txstate.edu/Volumes/2013/250/abstr.html |
| work_keys_str_mv |
AT mengrongli asymptoticbehaviorofpositivesolutionsofthenonlineardifferentialequationt2uun AT hsinyuyao asymptoticbehaviorofpositivesolutionsofthenonlineardifferentialequationt2uun AT yutsoli asymptoticbehaviorofpositivesolutionsofthenonlineardifferentialequationt2uun |
| _version_ |
1716776907317444608 |