English

Multispike solutions for the Brezis-Nirenberg problem in dimension three

Analysis of PDEs 2017-08-07 v1

Abstract

We consider the problem Δu+λu+u5=0\Delta u + \lambda u +u^5 = 0, u>0u>0, in a smooth bounded domain Ω\Omega in R3{\mathbb R}^3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at kk different points of the domain as λ\lambda tends to a special positive value λ0\lambda_0, which we characterize in terms of the Green function of Δλ-\Delta - \lambda.

Keywords

Cite

@article{arxiv.1708.01331,
  title  = {Multispike solutions for the Brezis-Nirenberg problem in dimension three},
  author = {M. Musso and D. Salazar},
  journal= {arXiv preprint arXiv:1708.01331},
  year   = {2017}
}

Comments

38 pages

R2 v1 2026-06-22T21:06:36.588Z