Description

• Title:
  Multi-bump solutions for a class of Kirchhoff type problems with critical growth in $\mathbb{R}^N$
• Creator:
  Liang, Sihua;
  Zhang, Jihui
• Description:
  Using variational methods, we establish existence of multi-bump solutions for a class of Kirchhoff type problems $$ -\bigg(1+b\int_{\mathbb{R}^N}|\nabla u|^pdx\bigg)\Delta_pu + (\lambda V(x) + Z(x))u^{p-1} = \alpha f(u) + u^{p^\ast-1}, $$ where $f$ is a continuous function, $V, Z\colon \mathbb{R}^N \rightarrow\mathbb{R}$ are continuous functions verifying some hypotheses. We show that if the zero set of $V$ has several isolated connected components $\Omega_1,\ldots,\Omega_k$ such that the interior of $\Omega_i$ is not empty and $\partial\Omega_i$ is smooth, then for $\lambda > 0$ large enough there exists, for any non-empty subset $\Gamma \subset \{1,\ldots,k\}$, a bump solution trapped in a neighbourhood of $\bigcup\limits_{j\in \Gamma}\Omega_j$. The results are also new for the case $p=2$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.05.29
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 48, No 1 (September 2016); 71 - 101;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.040/8903 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.040/8904
• Subject:
  Kirchhoff type problems;
  potential well;
  multi-bump solutions;
  variational methods;
  35J60;
  35Q55
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.040
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other