Description

• Title:
  Normalized solutions to a class of Choquard-type equations with potential
• Creator:
  Long, Lei;
  Feng, Xiaojing
• Description:
  In this paper, we study the existence and nonexistence of solutions to the following Choquard-type equation \begin{equation*} -\Delta u+(V+\lambda)u=(I_\alpha*F(u))f(u)\quad\text{in } \mathbb{R}^N, \end{equation*} having prescribed mass $\int_{\mathbb{R}^N}u^2=a$, where $\lambda\in\mathbb{R}$ will arise as a Lagrange multiplier, $N\geq 3$, $\alpha\in(0,N)$, $I_\alpha$ is Riesz potential. Under suitable assumptions on the potential function $V$ and the nonlinear term $f$, $a_0\in[0,\infty)$ exists such that the above equation has a positive ground state normalized solution if $a\in(a_0,\infty)$ and one has no ground state normalized solution if $a\in(0,a_0)$ when $a_0> 0$ by comparison arguments. Moreover, we obtain sufficient conditions for $a_0=0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Lei Long, Xiaojing Feng;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 2 (June 2024); 515 - 536;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49150/37882 ;https://apcz.umk.pl/TMNA/article/view/49150/37883
• Subject:
  Choquard-type equations;
  normalized solutions;
  positive solutions;
  Primary: 35D30, 35J20;
  Secondary: 35J50, 35Q55
• Identifier: https://apcz.umk.pl/TMNA/article/view/49150
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other