Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 112, pp. 1-14.

Title: Multiple solutions for a singular semilinear elliptic problems 
       with critical exponent and symmetries
       
Authors: Alfredo Cano (Univ. Autonoma del Estado de Mexico, Mexico)
         Sergio Hernandez-Linares (Univ. Autonoma Metropolitana, Mexico)
	 Eric Hernandez-Martinez (Univ. Autonoma de la ciudad de Mexico, Mexico)

Abstract:
 We consider the singular semilinear elliptic equation
 $$
 -\Delta u-\frac{\mu }{| x| ^2}u-\lambda u=f(x)| u| ^{2^{\ast }-1}
 $$ 
 in $\Omega $, $u=0$ on $\partial \Omega $,
 where $\Omega $  is a smooth bounded domain, in $\mathbb{R}^N$,
 $N\geq 4$, $2^{\ast }:=\frac{2N}{N-2}$ is the critical Sobolev
 exponent, $f:\mathbb{R} ^N\to \mathbb{R}$ is a continuous function,
 $0<\lambda <\lambda _1$, where $\lambda _1$ is the first
 Dirichlet eigenvalue of $-\Delta -\frac{\mu }{| x| ^2}$ in
 $\Omega $ and $0<\mu < \overline{\mu }:=(\frac{N-2}{2})^2$.
 We show that if $\Omega $ and $f$ are invariant under a subgroup
 of $O(N)$, the effect of the equivariant topology of $\Omega $ will
 give many symmetric nodal solutions, which extends previous results of
 Guo and Niu [8].

Submitted November 15, 2009. Published August 16, 2010.
Math Subject Classifications: 35J20, 35J25, 49J52, 58E35,74G35.
Key Words: Critical points; critical Sobolev exponent;
           multiplicity of solutions; invariant under the action 
	   of a orthogonal group; Palais-Smale condition; 
           singular semilinear elliptic problem; relative category.