Description

• Title:
  Multiple mixed interior and boundary peaks synchronized solutions for linearly coupled Schrödinger systems
• Creator:
  Jin, Ke
• Description:
  In the present paper we consider the problem: \begin{equation} \label{0}\tag{N$_\varepsilon$} \begin{cases} -\varepsilon^{2}\Delta u+u=u^{3}+\lambda v& \text{in } \Omega, \\ -\varepsilon^{2}\Delta v+v=v^{3}+\lambda u& \text{in } \Omega,\\ u> 0,\ v> 0& \text{in } \Omega,\\ \dfrac{\partial u}{\partial n}=\dfrac{\partial v}{\partial n}=0& \text{on } \partial\Omega, \end{cases} \end{equation} where $\varepsilon> 0$, $0< \lambda< 1$, $\Omega\subset\mathbb{R}^{3}$ is smooth and bounded, and $n$ denotes the outer normal vector defined on $\partial\Omega$, the boundary of $\Omega$. By the Lyapunov-Schmidt reduction method and the maximum principle of elliptic equations, we construct synchronized solutions of (\ref{0}) with mixed interior and boundary peaks for any $0< \varepsilon< \varepsilon_0$ and $\lambda\in(0,1)\backslash\{\lambda_0\}$, where $\lambda_0\in(0,1)$ is given and $\varepsilon_0> 0$ is sufficiently small. As $\varepsilon$ approaches $0$, the interior peaks concentrate at sphere packing points in $\Omega$ and the boundary peaks concentrate at the critical points of the mean curvature function of the boundary.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Ke Jin
• 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); 693 - 726;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/47719/37300 ;https://apcz.umk.pl/TMNA/article/view/47719/37301
• Subject:
  Schrödinger system;
  linearly coupled terms;
  mixed multiple spikes;
  35J20, 35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/47719
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other