Description

• Title:
  Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold
• Creator:
  Xu, Liping;
  Chen, Haibo
• Description:
  We investigate the following nonlinear biharmonic equations with pure power nonlinearities: \begin{equation*} \begin{cases} \triangle^2u-\triangle u+V(x)u= u^{p-1}u &\text{in } \mathbb{R}^N,\\ u> 0 &\text{for } u\in H^2(\mathbb{R}^N), \end{cases} \end{equation*} where $2< p< 2^*={2N}/({N-4})$. Under some suitable assumptions on $V(x)$, we obtain the existence of ground state solutions. The proof relies on the Pohožaev-Nehari manifold, the monotonic trick and the global compactness lemma, which is possibly different to other papers on this problem. Some recent results are extended.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.11.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 2 (December 2018); 541 - 560;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.015/15954 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.015/15955
• Subject:
  Biharmonic equations;
  ground state solutions;
  concentration-compactness principle;
  Pohožaev manifold;
  Nehari manifold;
  35J20;
  35J65;
  35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.015
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other