Description

• Title:
  On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
• Creator:
  Chabrowski, Jan;
  Szulkin, Andrzej
• Description:
  We consider the semilinear Schrödinger equation $$ -\Delta_A u+V(x)u =Q(x)|u|^{2^{*}-2}u. $$ Assuming that $V$ changes sign, we establish the existence of a solution $u\ne 0$ in the Sobolev space $ H_{A,V^+}^{1}(\RN)$. The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator $-\Delta_A$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2005.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 25, No 1 (March 2005); 3 - 21;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.001/9252
• Subject:
  Semilinear Schrödinger equation;
  critical Sobolev exponent;
  magnetic field;
  linking;
  35B33;
  35J65;
  35Q55
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.001
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other