Abstract

We describe as ε → 0 radially symmetric sign-changing solutions to the problem -Δu = |u|4/N - 2 - ε u in B where B is the unit ball in ℝN, N ≥ 3, under zero Dirichlet boundary conditions. We construct radial solutions with k nodal regions which resemble a superposition of "bubbles" of different signs and blow-up orders, concentrating around the origin. A dual phenomenon is described for the slightly supercritical problem -Δu = |u|4/N - 2 + ε u in ℝN \ B under Dirichlet and fast vanishing-at-infinity conditions.