Description

• Title:
  Some multiplicity results for a superlinear elliptic problem in $\mathbb R^N$
• Creator:
  Salvatore, Addolorata
• Description:
  In this paper we shall study the semilinear elliptic problem $$ \cases -\Delta u +\sigma(x)u= |u|^{p-2}u + f(x) & \text{in }\mathbb R^N,\\ u\rightarrow 0\quad\text{as } |x| \rightarrow\infty, \endcases $$ where $\sigma(x) \rightarrow\infty$ as $| x| \rightarrow\infty$, $p> 2$ and $f\in L^{2}(\mathbb R^{N})$. Thanks to a compact embedding of a suitable weigthed Sobolev space in $L^{2}(\mathbb R^{N})$, a direct use of the Symmetric Mountain Pass Theorem (if $f=0$) and of the fibering method (if $f\neq0$) allows to extend some multiplicity results, already known in the case of bounded domains.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 21, No 1 (March 2003); 29 - 39;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.002/9613
• Subject:
  Nonlinear Schrödinger equation;
  weighted Sobolev spaces;
  critical point theory;
  fibering method;
  35Q55;
  35J20;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.002
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other