Description

• Title:
  Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains
• Creator:
  Bieganowski, Bartosz;
  Secchi, Simone
• Description:
  We show that ground state solutions to the nonlinear, fractional problem \begin{equation*} \begin{cases} (-\Delta)^{s} u + V(x) u = f(x,u) & \text{in } \Omega, \\ u = 0 & \text{in } \R^N \setminus \Omega, \end{cases} \end{equation*} on a bounded domain $\Omega \subset \R^N$, converge (along a subsequence) in $L^2 (\Omega)$, under suitable conditions on $f$ and $V$, to a solution of the local problem as $s \to 1^-$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.10
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 2 (June 2021); 413 - 425;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.038/28176 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.038/28177
• Subject:
  Variational methods;
  fractional Schrödinger equation;
  non-local to local transition;
  ground state;
  Nehari manifold;
  Primary;
  35Q55;
  Secondary;
  35A15;
  35R11
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.038
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other