A refined result on sign changing solutions for a critical elliptic problem

In this work, we consider sign changing solutions to the critical elliptic problem Δu + |u|4/N-2 u = 0 in Ωε and u = 0 on δΩε, where Ωε := Ω-(∪_i=1 ^m (a_i +εΩ_i)) for small parameter ε > 0 is a perforated domain, Ω and Ω_i with 0 εΩ_i (∀i = 1; ⋯ ;m) are bounded regular general domains without symmetry in ℝ^N and a_i are points in Ω for all i = 1; ⋯ ;m. As ε goes to zero, we construct by gluing method solutions with multiple blow up at each point a _i for all i = 1; ⋯ ;m.