Description

• Title:
  Sign changing solutions of nonlinear Schrödinger equations
• Creator:
  Bartsch, Thomas;
  Wang, Zhi-Qiang
• Description:
  We are interested in solutions $u\in H^1({\mathbb R}^N)$ of the linear Schrödinger equation $-\delta u +b_{\lambda} (x) u =f(x,u)$. The nonlinearity $f$ grows superlinearly and subcritically as $\vert u\vert \to\infty$. The potential $b_{\lambda}$ is positive, bounded away from $0$, and has a potential well. The parameter $\lambda$ controls the steepness of the well. In an earlier paper we found a positive and a negative solution. In this paper we find third solution. We also prove that this third solution changes sign and that it is concentrated in the potential well if $\lambda \to \infty$. No symmetry conditions are assumed.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  1999.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 13, No 2 (June 1999); 191 - 198;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.010/10033
• Subject:
  Nonlinear Schrödinger equation;
  sign changing solution;
  localized solution;
  potential well;
  singular limit;
  Primary 35Q55;
  Secondary 35J65
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other