Electron. J. Diff. Eqns., Vol. 2007(2007), No. 84, pp. 1-6.

An existence result for elliptic problems with singular critical growth

Yasmina Nasri

Abstract:
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.

Submitted February 6, 2007. Published June 6, 2007.
Math Subject Classifications: 35J20, 35J60.
Key Words: Palais-Smale condition; singular potential; Sobolev exponent; mountain-pass theorem.

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Yasmina Nasri
Université de Tlemcen, département de mathématiques
BP 119 Tlemcen 13000, Algérie
email: y_nasri@mail.univ-tlemcen.dz

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