Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology

Mónica Clapp; Jorge Faya

Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology

Analysis of PDEs 2012-12-21 v1

Authors: Mónica Clapp , Jorge Faya

Abstract

We show that in every dimension $N\geq3$ there are many bounded domains $\Omega\subset\mathbb{R}^{N}$ , having only finite symmetries, in which the Bahri-Coron problem $-\Delta u=|u| ^{4/(N-2)}u\text{\in}\Omega,\text{\ \}u=0\text{\ on}\partial\Omega,$ has a prescribed number of solutions, one of them being positive and the rest sign changing.

Keywords

bahri-coron problem multiple solutions critical exponent bounded domains nontrivial topology sign changing solutions

Cite

@article{arxiv.1212.5130,
  title  = {Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology},
  author = {Mónica Clapp and Jorge Faya},
  journal= {arXiv preprint arXiv:1212.5130},
  year   = {2012}
}

Comments

To appear in Proceedings of the American Mathematical Society

Related papers

View all related →