Opis

• Title:
  An eigenvalue semiclassical problem for the Schrödinger operator with an electrostatic field
• Creator:
  D'Aprile, Teresa
• Description:
  We consider the following system of Schrödinger-Maxwell equations in the unit ball $B_1$ of ${\mathbb R}^3$ $$ -\frac{\hbar^2}{2m}\Delta v+ e\phi v=\omega v, \quad -\Delta\phi=4\pi e v^2 $$ with the boundary conditions $ u=0$, $ \phi=g$ on $\partial B_1$, where $\hbar$, $m$, $e$, $\omega > 0$, $v$, $\phi\colon B_1\rightarrow {\mathbb R}$, $g\colon \partial B_1\to {\mathbb R}$. Such system describes the interaction of a particle constrained to move in $B_1$ with its own electrostatic field. We exhibit a family of positive solutions $(v_\hbar, \phi_\hbar)$ corresponding to eigenvalues $\omega_\hbar$ such that $v_\hbar$ concentrates around some points of the boundary $\partial B_1$ which are minima for $g$ when $\hbar\rightarrow 0$.
• Object availability:
  Dostęp otwarty
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2006.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  angielski
• Source:
  Topological Methods in Nonlinear Analysis; Vol 27, No 1 (March 2006); 149 - 175;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.006/8880
• Subject:
  Schrödinger-Maxwell system;
  existence;
  concentration;
  35J20;
  35J60;
  35J55
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.006
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  poproś o pozwolenie
• Type:
  pozostałe