We consider the problemN −2 is the critical Sobolev exponent, and a, f are continuous functions. We assume that Ω, a and f are invariant under the action of a group of orthogonal transformations. We obtain multiplicity results which contain information about the symmetry and symmetry-breaking properties of the solutions, and about their nodal domains. Our results include new multiplicity results for the Brezis-Nirenberg problem − u + λu = |u| 2 * −2 u in Ω, u = 0 on ∂Ω.

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