Geodesic
An existence result for elliptic problems with singular critical growth
Electronic journal of differential equations, Tome 2007 (2007)
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 
@article{EJDE_2007__2007__a121,
     author = {Nasri,  Yasmina},
     title = {An existence result for elliptic problems with singular critical growth},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1133.35036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a121/}
}
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%A Nasri,  Yasmina
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%J Electronic journal of differential equations
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%V 2007
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%F EJDE_2007__2007__a121
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__a121/