Description

• Title:
  Neumann condition in the Schrödinger-Maxwell system
• Creator:
  Pisani, Lorenzo;
  Siciliano, Gaetano
• Description:
  We study a system of (nonlinear) Schrödinger and Maxwell equation in a bounded domain, with a Dirichelet boundary condition for the wave function $\psi$ and a nonhomogeneous Neumann datum for the electric potential $\phi$. Under a suitable compatibility condition, we establish the existence of infinitely many static solutions $\psi=u(x)$ in equilibrium with a purely electrostatic field ${\bold E}=-\nabla\phi$. Due to the Neumann condition, the same electric field is in equilibrium with stationary solutions $\psi=e^{-i\omega t}u(x)$ of arbitrary frequency $\omega$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2007.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 29, No 2 (June 2007); 251 - 264;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.010/8832
• Subject:
  Schrödinger equation;
  stationary solutions;
  electrostatic field;
  variational methods;
  eigenvalue problem;
  Primary 35J50;
  35J65;
  Secondary 35Q55;
  35Q60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other