Abstract

Let B denote the unit ball in ℝ2. We consider the slightly super-critical Gelfand problem for the p-Laplacian operator Δpu = div (|∇u|p-2∇u), - Δ2- εu = λ eu in B, u = 0 on ∂B, for small ε > 0. We show that if k ≥ 1 is given and λ > 0 is fixed and small, then there is a family of radial solutions exhibiting multiple blow-up as ε → 0 in the form of a superposition of k bubbles of different blow-up orders and shapes. Similar phenomena is found for the same problem involving the operator ΔN-ε in ℝN, N ≥ 3.