Geodesic
A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term
Electronic journal of differential equations, Tome 2007 (2007)
Via a sub-supersolution method and a perturbation argument, we study the Lane-Emden-Fowler equation

$ -\Delta u =p(x)[g(u)+f(u)+|\nabla u|^q] $

in $\mathbb{R} ^N (N\geq3)$, where $0 less than q less than 1, p$ is a positive weight such that $\varphi(r)=\max_{|x|=r}p(x), r\geq 0$. Under the hypotheses that both $g$ and $f$ are sublinear, which include no monotonicity on the functions $g(u), f(u), g(u)/u$ and $f(u)/u$, we show the existence of ground state solutions.
Classification : 35J60, 35B25, 35B50, 35R05
Keywords: ground state solution, Lane-Emden-Fowler equation, convection term, maximum principle, existence, sub-solution, super-solution 
@article{EJDE_2007__2007__a106,
     author = {Xue,  Hongtao and Zhang,  Zhijun},
     title = {A remark on ground state solutions for {Lane-Emden-Fowler} equations with a convection term},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1129.35035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/}
}
TY  - JOUR
AU  - Xue,  Hongtao
AU  - Zhang,  Zhijun
TI  - A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term
JO  - Electronic journal of differential equations
PY  - 2007
VL  - 2007
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/
LA  - en
ID  - EJDE_2007__2007__a106
ER  - 
%0 Journal Article
%A Xue,  Hongtao
%A Zhang,  Zhijun
%T A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/
%G en
%F EJDE_2007__2007__a106
Xue,  Hongtao; Zhang,  Zhijun. A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/