Description

• Title:
  Nonlinear scalar field equations in $\mathbb{R}^{N}$: mountain pass and symmetric mountain pass approaches
• Creator:
  Hirata, Jun;
  Ikoma, Norihisa;
  Tanaka, Kazunaga
• Description:
  We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in $\mathbb{R}^N$: \begin{gather*} -\Delta u=g(u) \quad \text{in }\mathbb{R}^N,\\ u\in H^1(\mathbb R^N). \end{gather*} We give an extension of the existence results due to H. Berestycki, T. Gallouët and O. Kavian [< i> Equations de Champs scalaires euclidiens non linéaires dans le plan< /i> , C. R. Acad. Sci. Paris Ser. I Math. < b> 297< /b> , 307–310].< /p>< p> We take a mountain pass approach in $H^1(\mathbb{R}^N)$ and introduce a new method generating a Palais-Smale sequence with an additional property related to Pohozaev identity.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 2 (June 2010); 253 - 276;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.015/8442
• Subject:
  Nonlinear scalar field equations;
  radially symmetric solutions;
  minimax methods;
  Primary 35J20;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.015
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other