Article - postprint
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>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.
© 2003 IOP Publishing
Castro, Alfonso and Monica Clapp. “The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain”, Nonlinearity 16(2003), 579-590.