Description

• Title:
  Semiclassical solutions for fractional logarithmic Schrödinger equations with potentials unbounded below
• Creator:
  An, Xiaoming;
  Yang, Xian
• Description:
  In this paper, we consider the following fractional logarithmic Schrödinger equation \begin{equation*} \varepsilon^{2s}(-\Delta)^s u + V(x)u=u\log u^2\quad \text{in } \R^N, \end{equation*} where $\varepsilon> 0$, $N\ge 1$ and $V(x)\in C\big(\R^N,\R\big)$ is a potential which can be unbounded below at infinity. By considering a new penalization, we show that the problem has a nontrivial solution $u_{\varepsilon}$ concentrating at a local minimum of $V$ as $\varepsilon\to 0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Xiaoming An, Xian Yang;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.09.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 383 - 407;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55336/39776 ;https://apcz.umk.pl/TMNA/article/view/55336/39777
• Subject:
  Fractional logarithmic Schrödinger;
  penalization;
  concentration;
  unbounded below;
  Primary: 35J05, 35J20;
  Secondary: 35J10
• Identifier: https://apcz.umk.pl/TMNA/article/view/55336
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other