Description

• Title:
  Normalized solutions for the Schrödinger-Poisson system with doubly critical growth
• Creator:
  Meng, Yuxi;
  He, Xiaoming
• Description:
  In this paper we are concerned with normalized solutions to the Schrödinger-Poisson system with doubly critical growth \[ \begin{cases} -\Delta u-\phi |u|^3u=\lambda u+\mu|u|^{q-2}u+|u|^4u, &x \in \R^{3},\\ -\Delta \phi=|u|^5, &x \in \R^{3}, \end{cases} \] and prescribed mass \[ \int_{\R^3}|u|^2dx=a^2,\] where $a> 0$ is a constant, $\mu> 0$ is a parameter and $2< q< 6$. In the $L^2$-subcritical case, we study the multiplicity of normalized solutions by applying the truncation technique, and the genus theory; and in the $L^2$-supercritical case, we obtain a couple of normalized solutions by developing a fiber map. Under both cases, to recover the loss of compactness of the energy functional caused by the critical growth, we need to adopt the concentration-compactness principle. Our results complement and improve some related studies for the Schrödinger-Poisson system with nonlocal critical term in the literature.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Yuxi Meng, Xiaoming He;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.12.31
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 62, No 2 (December 2023); 509 - 534;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/47706/37274 ;https://apcz.umk.pl/TMNA/article/view/47706/37275
• Subject:
  Schrödinger-Poisson system;
  normalized solutions;
  variational methods;
  L^2-subcritical;
  L^2-supercritical;
  35A15, 35B33, 35J20, 35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/47706
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other