Multispike solutions for the Brezis-Nirenberg problem in dimension three

M. Musso, D. Salazar

Published 2017-08-03Version 1

We consider the problem $\Delta u + \lambda u +u^5 = 0$, $u>0$, in a smooth bounded domain $\Omega$ 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 $\lambda$ tends to a special positive value $\lambda_0$, which we characterize in terms of the Green function of $-\Delta - \lambda$.