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__a68,
     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__a68/}
}
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%A Kar,  Rasmita
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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__a68/