Description

• Title:
  Existence of positive solutions for generalized fractional Brézis-Nirenberg problem
• Creator:
  Kumar, Rohit;
  Sarkar, Abhishek
• Description:
  In this article, we study the fractional Brézis-Nirenberg type problem on whole domain $\R^N$ associated with the fractional $p$-Laplace operator. To be precise, we want to study the following problem: \begin{equation} \label{Pr1} (-\Delta_{p})^{s}u - \lambda w |u|^{p-2}u= |u|^{p_{s}^{*}-2}u \quad \text{in } \mathcal{D}^{s,p}\big(\mathbb{R}^{N}\big) , \tag{P} \end{equation} where $s\in (0,1), p\in (1, {N}/{s})$, $p_{s}^{*}={Np}/({N-sp})$ and the operator $(-\Delta_{p})^{s}$ is the fractional $p$-Laplace operator. The space $\mathcal{D}^{s,p}\big(\mathbb{R}^{N}\big)$ is the completion of $C_c^\infty\big(\R^N\big)$ with respect to the Gagliardo semi-norm. In this article, we prove the existence of a positive solution to problem \eqref{Pr1} by allowing the Hardy weight function $w$ to change its sign.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Rohit Kumar, Abhishek Sarkar
• Date:
  2024.09.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 509 - 543;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55344/39792 ;https://apcz.umk.pl/TMNA/article/view/55344/39793
• Subject:
  Fractional Brézis-Nirenberg problem;
  critical Sobolev exponent;
  concentration compactness;
  principle of symmetric criticality;
  positive solutions;
  35B09,35R11
• Identifier: https://apcz.umk.pl/TMNA/article/view/55344
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other