Description

• Title:
  Equation with positive coefficient in the quasilinear term and vanishing potential
• Creator:
  Aires, Jose;
  Souto, Marco A. S.
• Description:
  In this paper we study the existence of nontrivial classical solution forthe quasilinear Schr\"odinger equation: $$ - \Delta u +V(x)u+\frac{\kappa}{2}\Delta(u^{2})u= f(u), $$%in $\mathbb{R}^N$, where $N\geq 3$, $f$ hassubcritical growth and $V$ is a nonnegative potential. For this purpose, we use variational methods combined with perturbation arguments, penalization technics of Del Pino and Felmer and Moser iteration. As a main novelty with respect to some previous results, in our work we are able to deal with the case $\kappa > 0$ and the potential can vanish at infinity.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 813 - 834;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.069/7266 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.069/7303
• Subject:
  Quasilinear Schrodinger equation;
  subcritical growth;
  Vanishing potentials;
  35J20;
  35J65
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.069
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other