Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries

Abstract

We consider the singular semilinear elliptic equation on where is a smooth bounded domain,in the critical Sobolev exponent ; a continuous function where is the rst Dirichlet eigen value of in and We show that if and are invariant under a subgroup of the efect of the equivariant topology o will give many symmetric nodal solutions , which extends previous results of Guo and Niu.