The Effect of the Domain Topology on the Number of Minimal Nodal Solutions of an Elliptic Equation at Critical Growth in a Symmetric Domain

We consider the Dirichlet problem Δu + λu + |u|2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in RN, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ\u3e0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once