Description

• Title:
  Multiple solutions to Bahri-Coron problem involving fractional $p$-Laplacian in some domain with nontrivial topology
• Creator:
  Kumar, Uttam;
  Tiwari, Sweta
• Description:
  In this article, we establish the existence of positive and multiple sign-changing solutions to the fractional $p$-Laplacian equation with purely critical nonlinearity \begin{equation} \label{Ppomegas-a}\tag{P$_{p,\Omega}^{s}$} \begin{cases} (-\Delta)_{p}^s u =|u|^{p_s^*-2} u& \text{in }\Omega, \\ u =0 & \text{on }\Omega^{c}, \end{cases} \end{equation} in a bounded domain $\Omega\subset \mathbb{R}^{N}$ for $s\in (0,1)$, $p\in (1,\infty)$, and the fractional critical Sobolev exponent $p^{*}_{s}={Np}/({N-sp})$ under some symmetry assumptions. We study Struwe's type global compactness results for the Palais-Smale sequence in the presence of symmetries.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Uttam Kumar, Sweta Tiwari
• Date:
  2023.06.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 2 (June 2023); 717 - 742;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/44694/35877 ;https://apcz.umk.pl/TMNA/article/view/44694/35878
• Subject:
  Non-local problem;
  fractional p-Laplacian;
  critical exponent;
  global compactness;
  Primary: 35A15, 35A16, 35B33, 35J60, 35R11;
  Secondary: 35J20
• Identifier: https://apcz.umk.pl/TMNA/article/view/44694
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other