Geodesic
Weak solutions for degenerate semilinear elliptic BVPs in unbounded domains
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: In this article, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$\displaylines{ Lu(x)+\sum_{i=1}^n g(x)h(u(x))D_iu(x)=f(x)\quad \hbox{in }\Omega,\cr u=0\quad \hbox{on }\partial\Omega, }$$ in a suitable weighted Sobolev space. Here $\Omega\subset\mathbb{R}^n, 1\leq n\leq3,$ is not necessarily bounded.
Classification : 46E35, 35J61
Keywords: semilinear elliptic boundary value problem, unbounded domain, pseudomonotone operator 
@article{EJDE_2012__2012__a57,
     author = {Kar, Rasmita},
     title = {Weak solutions for degenerate semilinear elliptic {BVPs} in unbounded domains},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a57/}
}
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Kar, Rasmita. Weak solutions for degenerate semilinear elliptic BVPs in unbounded domains. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a57/