Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 84, pp. 1-6.
Title: An existence result for elliptic
problems with singular critical growth
Author: Yasmina Nasri (Univ. de Tlemcen, Algerie)
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.