Geodesic
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
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     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a68/}
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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/