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The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp

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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 R^N, 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>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.