A note on the number of nodal solutions of an elliptic equation with symmetry

We consider the semilinear problem −Δu+λu=|u|p−2u in ΩΩ, u=0u=0 on ∂Ω∂Ω, where Ω⊂RNΩ⊂RN is a bounded smooth domain and 20λ>0 sufficiently large, the equivariant topology of ΩΩ is related to the number of solutions which change sign exactly once.