Multispike solutions for the Brezis-Nirenberg problem in dimension three

Abstract

We consider the problem $Δu + λu +u^5 = 0$, $u>0$, in a smooth bounded domain $Ω$ in ${\mathbb R}^3$, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at $k$ different points of the domain as $λ$ tends to a special positive value $λ_0$, which we characterize in terms of the Green function of $-Δ- λ$.

38 pages