Geodesic
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains
Electronic journal of differential equations, Tome 2009 (2009)
In this study, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem

$\displaylines{ Lu-\mu u g_{1} + h(u) g_{2}= f\quad \hbox{in }\Omega,\cr u = 0\quad \hbox{on }\partial\Omega }$

in a suitable weighted Sobolev space. Here the domain $\Omega\subset\mathbb{R}^{n}, n\geq 3$, is not necessarily bounded, and $h$ is a continuous bounded nonlinearity. The theory is also extended for $h$ continuous and unbounded.
Classification : 35J70, 35D30
Keywords: degenerate equations, weighted Sobolev space, unbounded domain 
@article{EJDE_2009__2009__a168,
     author = {Raghavendra,  Venkataramanarao and Kar,  Rasmita},
     title = {Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1189.35132},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a168/}
}
TY  - JOUR
AU  - Raghavendra,  Venkataramanarao
AU  - Kar,  Rasmita
TI  - Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains
JO  - Electronic journal of differential equations
PY  - 2009
VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a168/
LA  - en
ID  - EJDE_2009__2009__a168
ER  - 
%0 Journal Article
%A Raghavendra,  Venkataramanarao
%A Kar,  Rasmita
%T Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a168/
%G en
%F EJDE_2009__2009__a168
Raghavendra,  Venkataramanarao; Kar,  Rasmita. Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a168/