Description

• Title:
  Multiple solutions to the Bahri-Coron problem in the complement of a thin tubular neighbourhood of a manifold
• Creator:
  Clapp, Monica;
  Fernández, Juan Carlos
• Description:
  We show that the critical problem% \[ -\Delta u=|u|^{{{4}}/({{N-2}})}u\quad \text{in }\Omega,\qquad\ u=0\quad \text{on }\partial\Omega, \] has at least% \[ \max\{\text{cat}(\Theta,\Theta\setminus B_{r}M),\text{cupl}(\Theta ,\Theta\setminus B_{r}M)+1\}\geq2 \] pairs of nontrivial solutions in every domain $\Omega$ obtained by deleting from a~given bounded smooth domain $\Theta\subset\mathbb{R}^{N}$ a thin enough tubular neighborhood $B_{r}M$ of a closed smooth submanifold $M$ of $\Theta$ of dimension $\leq N-2$, where ``cat'' is the Lusternik-Schnirelmann category and ``cupl'' is the cup-length of the pair.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 1119 - 1138;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.085/7344 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.085/7346
• Subject:
  Nonlinear elliptic boundary value problem;
  critical nonlinearity;
  multiple solutions;
  perturbed domain;
  fixedpoint transfer;
  35J91;
  35J20;
  35J25
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.085
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other