Description

• Title:
  Concentrating solutions for a class of indefinite Schrödinger-Poisson systems with doubly critical growth
• Creator:
  Shen, Liejun;
  Squassina, Marco
• Description:
  We study the following Schrödinger-Poisson system involving critical nonlocal term with indefinite steep potential well $$ \begin{cases} -\Delta u+(\lambda V(x)-\mu)u-\phi |u|^3u= f(u), & x\in\R^3, \\ -\Delta \phi= |u|^5, & x\in\R^3, \end{cases} $$% where $\lambda> 0$ is a parameter, $V\in \mathcal{C}\big(\R^3,\R^+\big)$ admits a potential well $\Omega \triangleq\text{int}V^{-1}(0)$, and $\mu> \mu_1$ is a constant such that the operator $L_\lambda \triangleq -\Delta + \lambda V-\mu$ is non-degenerate when $\lambda$ is large enough with $\{\mu_j\}_{j=1}^\infty$ denoting the Dirichlet eigenvalues of $\big(-\Delta,H_0^1(\Omega)\big)$. If $f$ satisfies some suitable assumptions involving critical growth, with the help of a linking-type result involving the modified Pankov-Nehari manifold procedure, we establish the existence and concentrating behavior of positive solutions for the given system using variational methods.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2025 Liejun Shen, Marco Squassina;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 33;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62313/42827 ;https://apcz.umk.pl/TMNA/article/view/62313/42828
• Subject:
  Schrödinger-Poisson system;
  critical nonlocal term;
  indefinite variational problem;
  linking;
  modified Pankov-Nehari manifold;
  concentrating;
  Primary: 35J15, 35J20;
  Secondary: 35B06
• Identifier: https://apcz.umk.pl/TMNA/article/view/62313
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other