SIGN-CHANGING TOWER OF BUBBLES FOR THE BREZIS-NIRENBERG PROBLEM

In this paper, we prove that the Brezis–Nirenberg problem: −Δu = |u|p−1u + ϵuinΩ,u = 0on∂Ω, where Ω is a symmetric bounded smooth domain in ℝN, N ≥ 7 and p = N+2 N−2, has a solution with the shape of a tower of two bubbles with alternate signs, centered at the center of symmetry of the domain, for all ϵ > 0 sufficiently small.