Description

• Title:
  Fractional Hardy-Sobolev elliptic problems
• Creator:
  Yang, Jianfu;
  Yu, Xiaohui
• Description:
  In this paper, we study the following singular nonlinear elliptic problem \begin{equation} \begin{cases} \displaystyle (-\Delta)^{ \alpha/ 2} u=\lambda |u|^{r-2}u+\mu\frac{|u|^{q-2}u}{|x|^{s}} &\text{in }\Omega, \\ u=0 &\text{on } \partial\Omega, \end{cases} \tag{P} \end{equation} where $\Omega$ is a smooth bounded domain in $\mathbb R^N(N\geq 2)$ with $0\in \Omega$, $\lambda,\mu> 0$, $0< s\leq\alpha$, $(-\Delta)^{\alpha/ 2}$ is the spectral fractional Laplacian operator with $0< \alpha< 2$. We establish existence results and nonexistence results of problem \eqref{eq:1} for subcritical, Sobolev critical and Hardy-Sobolev critical cases.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.03.04
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 55, No 1 (March 2020); 257 - 280;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.075/25000 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.075/25001
• Subject:
  Critical Hardy-Sobolev exponent;
  decaying law;
  existence;
  35J25;
  47G30;
  35B45;
  35J70
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.075
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other