Description

• Title:
  Existence of solutions for the Brezis-Nirenberg problem
• Creator:
  de Paiva, Francisco Odair;
  Miyagaki, Olímpio H.;
  Presoto, Adilson E.
• Description:
  We are concerned with of existence of solutions to the semilinear elliptic problem $$ \begin{cases} - \Delta u=\lambda_{k}u+u^3 &\text{in } \Omega, \\ u= 0 &\text{on }\partial \Omega, \end{cases} $$% in a bounded domain $\Omega \subset \mathbb{R}^{4}$. Here $\lambda_k$ is an eigenvalue of the $-\Delta$ in $H_0^1(\Omega)$. We prove that this problem has a nontrivial solution.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Francisco Odair de Paiva, Olímpio H. Miyagaki, Adilson E. Presoto;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.01.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 2 (June 2023); 651 - 659;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42232/34566 ;https://apcz.umk.pl/TMNA/article/view/42232/34567
• Subject:
  Critical growth;
  resonance;
  low dimension;
  Primary: 35J20, 35J61;
  Secondary: 35B33, 35B34
• Identifier: https://apcz.umk.pl/TMNA/article/view/42232
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other