Infinitely many non-radial solutions to a critical equation on annulus

In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem (P)−Δu=|u|[Formula presented]u, in Ω,u=0, on ∂Ω on the annulus Ω:=x∈RN:a<|x|<b, N≥3. In particular, for any integer k large enough, we build a non-radial solution which look like the unique positive solution u0to (P) crowned by k negative bubbles arranged on a regular polygon with radius r0such that r0[Formula presented]u0(r0)=:maxa≤r≤b⁡r[Formula presented]u0(r).