Description

• Title:
  Minimizers of L^2-critical inhomogeneous variational problems with a spatially decaying nonlinearity in bounded domains
• Creator:
  Zhang, Hongfei;
  Zhang, Shu
• Description:
  We consider the minimizers of $L^{2}$-critical inhomogeneous variational problems with a spatially decaying nonlinear term in an open bounded domain $\Omega$ of $\mathbb{R}^{N}$ which contains $0$. We prove that there is a threshold $a^{*}> 0$ such that minimizers exist for $0< a< a^{*}$ and the minimizer does not exist for any $a> a^{*}$. In contrast to the homogeneous case, we show that both the existence and nonexistence of minimizers may occur at the threshold $a^*$ depending on the value of $V(0)$, where $V(x)$ denotes the trapping potential. Moreover, under some suitable assumptions on $V(x)$, based on a detailed analysis on the concentration behavior of minimizers as $a\nearrow a^*$, we prove local uniqueness of minimizers when $a$ is close enough to $a^*$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Hongfei Zhang, Shu Zhang;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.06.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 1 (September 2024); 31 - 59;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/52726/38795 ;https://apcz.umk.pl/TMNA/article/view/52726/38796
• Subject:
  L^{2}-critical;
  spatially decaying nonlinear;
  minimizers;
  concentration behavior;
  local uniqueness;
  Primary: 35Q40, 46N50;
  Secondary: 35J20, 35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/52726
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other