Description

• Title:
  Singularly perturbed N-Laplacian problems with a nonlinearity in the critical growth range
• Creator:
  Zhang, Jianjun;
  do Ó, João Marcos;
  Miyagaki, Olímpio H.
• Description:
  We consider the following singularly perturbed problem: $$ -\e^N\Delta_N u+V(x)|u|^{N-2}u= f(u),\quad u(x)> 0\quad \mbox{in } \mathbb R^N, $$ \noindent where $N\ge 2$ and $\Delta_N u$ is the $N$-Laplacian operator. In this paper, we construct a solution $u_\e$ which concentrates around any given isolated positive local minimum component of $V$, as $\e\rg 0$, in the Trudinger-Moser type of subcritical or critical case. In the subcritical case, we only impose on $f$ the Berestycki and Lions conditions. In the critical case, a global condition on the nonlinearity $f$ is imposed. However, any {\it monotonicity} of $f(t)/t^{N-1}$ or {\it Ambrosetti-Rabinowitz} type conditions are not required.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.11.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 2 (December 2017); 553 - 579;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.021/13425 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.021/13426
• Subject:
  Nonlinear Schrödinger equations;
  semiclassical states;
  potential well;
  critical growth;
  penalization;
  Primary;
  35B25;
  35B33;
  Secondary;
  35J61
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.021
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other