Description

• Title:
  Quasilinear Schrödinger equations with singular and vanishing potentials involving nonlinearities with critical exponential growth
• Creator:
  Araújo, Yane Lísley;
  Carvalho, Gilson;
  Clemente, Rodrigo
• Description:
  In this paper, we study the following class of Schrödinger equations: \[ -\Delta_{N}u+V(|x|)|u|^{N-2}u=Q(|x|)h(u) \quad \text{in } \mathbb{R}^N, \] where $N\geq 2$, $V,Q\colon \mathbb{R}^{N}\rightarrow \mathbb{R}$ are potentials that can be unbounded, decaying or vanishing at infinity and the nonlinearity $h\colon \mathbb{R}\rightarrow \mathbb{R}$ has a critical exponential growth concerning the Trudinger-Moser inequality. By using a variational approach, a version of the Trudinger-Moser inequality and a symmetric criticality type result, we obtain the existence of nonnegative weak and ground state solutions for this class of problems and under suitable assumptions, we obtain a nonexistence result.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 317 - 342;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.024/28139 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.024/28140
• Subject:
  Variational methods;
  critical exponential growth;
  Schrödinger equation;
  unbounded or decaying potentials;
  Primary;
  35J20;
  35B33;
  Secondary;
  35J60;
  35J05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.024
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other