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 · Nonlinearity · 2003
We consider the Dirichlet problem Δ u +λ u +| u | 2*−2 u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in ℝ N , N ⩾4, and 2* = 2 N /( 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.