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

Abstract

In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem:(P){−Δu=|u|4N−2u, 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 u0 to (P) crowned by k negative bubbles arranged on a regular polygon with radius r0 such that r0N−22u0(r0)=:maxa≤r≤b⁡rN−22u0(r).