Description

• Title:
  Semiclassical states for critical Choquard equations with critical frequency
• Creator:
  Gao, Fashun;
  Zhou, Jiazheng
• Description:
  We study the multiplicity of semiclassical states for the Choquard equation $$ -\varepsilon^2\Delta u +V(x)u =\varepsilon^{\mu-N}\bigg(\int_{\mathbb{R}^{N}} \frac{G(y,u(y))}{|x-y|^\mu}dy\bigg)g(x,u) \quad \mbox{in $\mathbb{R}^{N}$}, $$ where $0< \mu< N$, $N\geq3$, $\varepsilon$ is a positive parameter and $G$ is the primitive of $g$ which is of critical growth due to the Hardy-Littlewood-Sobolev inequality. The potential function $V$ is assumed to be nonnegative with $V(x)=0$ in some region of $\mathbb{R}^{N}$. Using the genus theory we prove the multiplicity of semiclassical states for the critical Choquard equation.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.20
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 107 - 133;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.001/28250 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.001/28251
• Subject:
  Critical Choquard equation;
  Hardy-Littlewood-Sobolev inequality;
  semiclassical states;
  critical frequency;
  35J20;
  35J60;
  35A15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.001
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other