Description

• Title:
  On semiclassical ground states for Hamiltonian elliptic system with critical growth
• Creator:
  Zhang, Jian;
  Tang, Xianhua;
  Zhang, Wen
• Description:
  In this paper, we study the following Hamiltonian elliptic system with gradient term and critical growth: \begin{equation*} \begin{cases} -\epsilon^{2}\Delta \psi +\epsilon b\cdot \nabla \psi +\psi=K(x)f(|\eta|)\varphi+W(x)|\eta|^{2^*-2}\varphi &\hbox{in} \mathbb{R}^{N},\\ -\epsilon^{2}\Delta \varphi -\epsilon b\cdot \nabla \varphi +\varphi=K(x)f(|\eta|)\psi+W(x)|\eta|^{2^*-2}\psi &\hbox{in} \mathbb{R}^{N}, \end{cases} \end{equation*} where $\eta=(\psi,\varphi)\colon \mathbb{R}^{N}\rightarrow\mathbb{R}^{2}$, $K, W\in C(\mathbb{R}^{N}, \mathbb{R})$, $\epsilon$ is a small positive parameter and $b$ is a constant vector. We require that the nonlinear potentials $K$ and $W$ have at least one global maximum. Combining this with other suitable assumptions on $f$, we prove the existence, exponential decay and concentration phenomena of semiclassical ground state solutions for all sufficiently small $\epsilon> 0$
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.10.24
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 1 (March 2017); 245 - 272;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.069/10213 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.069/10214
• Subject:
  Hamiltonian elliptic systems;
  semiclassical ground states;
  concentration;
  critical growth;
  35J50;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.069
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other