Geodesic
Asymptotic behavior of positive solutions of the nonlinear differential equation \(t^2u''=u^n\)
Electronic journal of differential equations, Tome 2013 (2013)
In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1$, 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.
Classification : 34A34, 34C11, 34C60
Keywords: nonlinear differential equation, Emden-Fowler equation, blow-up rate 
@article{EJDE_2013__2013__a88,
     author = {Li,  Meng-Rong and Yao,  Hsin-Yu and Li,  Yu-Tso},
     title = {Asymptotic behavior of positive solutions of the nonlinear differential equation \(t^2u''=u^n\)},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1293.34064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a88/}
}
TY  - JOUR
AU  - Li,  Meng-Rong
AU  - Yao,  Hsin-Yu
AU  - Li,  Yu-Tso
TI  - Asymptotic behavior of positive solutions of the nonlinear differential equation \(t^2u''=u^n\)
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a88/
LA  - en
ID  - EJDE_2013__2013__a88
ER  - 
%0 Journal Article
%A Li,  Meng-Rong
%A Yao,  Hsin-Yu
%A Li,  Yu-Tso
%T Asymptotic behavior of positive solutions of the nonlinear differential equation \(t^2u''=u^n\)
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a88/
%G en
%F EJDE_2013__2013__a88
Li,  Meng-Rong; Yao,  Hsin-Yu; Li,  Yu-Tso. Asymptotic behavior of positive solutions of the nonlinear differential equation \(t^2u''=u^n\). Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a88/