Geodesic
An existence result for elliptic problems with singular critical growth
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: We prove the existence of nontrivial solutions for the singular critical problem $$ -\Delta u-\mu \frac{u}{|x|^{2}}=\lambda f(x)u+u^{2^{\ast }-1} $$ with Dirichlet boundary conditions. Here the domain is a smooth bounded subset of $\mathbb{R}^N, N\geq 3$, and $2^{\ast }=\frac{2N}{N-2}$ which is the critical Sobolev exponent.
Classification : 35J20, 35J60
Keywords: palais-Smale condition, singular potential, Sobolev exponent, mountain-pass theorem 
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     author = {Nasri, Yasmina},
     title = {An existence result for elliptic problems with singular critical growth},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a221/}
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Nasri, Yasmina. An existence result for elliptic problems with singular critical growth. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a221/