Description

• Title:
  Concentrating solutions for a biharmonic problem with supercritical growth
• Creator:
  Liu, Zhongyuan
• Description:
  In this paper we consider the following supercritical biharmonic problem: $$ \begin{cases} \Delta^2 u= K(x)u^{p+\epsilon}&\text{in } \Omega,\\ u> 0 &\text{in }\Omega,\\ u=\Delta u=0&\text{on }\partial\Omega, \end{cases} $$ where $K(x)\in C^3(\overline{\Omega})$ is a nonnegative function, $p=({N+4})/({N-4})$, $\epsilon> 0$, $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\geq6$. We show that, for $\epsilon$ small enough, there exists a family of concentrating solutions under certain assumptions on the critical points of the function $K(x)$.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Zhongyuan Liu
• Date:
  2023.12.31
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 62, No 2 (December 2023); 455 - 484;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/47711/37284 ;https://apcz.umk.pl/TMNA/article/view/47711/37285
• Subject:
  Concentrating solutions;
  biharmonic problem;
  supercritical growth;
  Primary: 35J30, 35J91;
  Secondary: 35J40, 31B30
• Identifier: https://apcz.umk.pl/TMNA/article/view/47711
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other