Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 122, pp. 1-14.
Title: Multiple symmetric solutions for a singular semilinear
elliptic problem with critical exponent
Authors: Alfredo Cano (Univ. Autonoma de Mexico, Mexico)
Eric Hernandez-Martinez (Univ. Autonoma de Mexico, Mexico)
Abstract:
Let be $\Gamma$ a closed subgroup of $O(N)$.
We consider the semilinear elliptic problem
$$\displaylines{
-\Delta u-\frac{b(x)}{| x|^2}u-a(x)u=f(x)| u|^{2^{\ast }-2}u\quad
\hbox{in }\Omega ,\cr
u=0 \quad\hbox{on } \partial \Omega ,
}$$
where $\Omega \subset \mathbb{R}^{N}$ is a smooth
bounded domain, $N\geq 4$.
We establish the multiplicity of symmetric positive solutions,
nodal solutions, and solutions which are $\Gamma$ invariant but
are not $\widetilde{\Gamma}$ invariant, where
$\Gamma \subset \widetilde{\Gamma}\subset O(N)$.
Submitted March 27, 2012. Published July 20, 2012.
Math Subject Classifications: 35J75, 35J57, 35J60.
Key Words: Critical exponent; singular problem; symmetric solutions.