LAUSR

Abstract We study the problem (Pα) − Δ u = | x | α | u | 4 + 2 α N − 2 − e u in  Ω , u = 0 on  ∂ Ω , where Ω is a bounded smooth domain in R N , N ≥ 3 , which is symmetric with respect to x 1 , x 2 , … , x N and contains the origin, α > 0 , and e > 0 is a small parameter. We construct solutions to ( P α ) with the shape of a sign-changing tower of bubbles of order α that concentrate and blow-up at the origin as e → 0 . We also study a slightly Henon supercritical dual version of ( P α ) in an exterior domain, for which we found solutions with the shape of a flat sign-changing tower of bubbles of order α that disappear as e → 0 .