Description

• Title:
  Bifurcation and multiplicity results for critical p-Laplacian problems
• Creator:
  Perera, Kanishka;
  Squassina, Marco;
  Yang, Yang
• Description:
  We prove a bifurcation and multiplicity result that is independent of the dimension N for a critical p-Laplacian problem that is the analog of the Brezis-Nirenberg problem for the quasilinear case. This extends a result in the literature for the semilinear case p = 2 to all p in (1;infty). In particular, it gives a new existence result when N \le p^2. When p \neq 2 the nonlinear operator -\Delta_p has no linear eigenspaces, so our extension is nontrivial and requires a new abstract critical point theorem that is not based on linear subspaces. We prove a new abstract result based on a pseudoindex related to the Z^2-cohomological index that is applicable here.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 1 (March 2016); 187 - 194;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.093/7518 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.093/7519
• Subject:
  p-Laplacian;
  critical nonlinearity;
  bifurcation;
  multiplicity;
  existence;
  abstract critical point theory;
  Z^2-cohomological index;
  pseudo-index;
  Primary;
  35J92;
  Secondary;
  35B33;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.093
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other