Affordable Access

$N$-Laplacian problems with critical Trudinger-Moser nonlinearities

Authors
  • Yang, Yang
  • Perera, Kanishka
Type
Preprint
Publication Date
Jan 03, 2016
Submission Date
Jun 24, 2014
Identifiers
arXiv ID: 1406.6242
Source
arXiv
License
Yellow
External links

Abstract

We prove existence and multiplicity results for a $N$-Laplacian problem with a critical exponential nonlinearity that is a natural analog of the Brezis-Nirenberg problem for the borderline case of the Sobolev inequality. This extends results in the literature for the semilinear case $N = 2$ to all $N \ge 2$. When $N > 2$ the nonlinear operator $- \Delta_N$ has no linear eigenspaces and hence this extension requires new abstract critical point theorems that are not based on linear subspaces. We prove new abstract results based on the ${\mathbb Z}_2$-cohomological index and a related pseudo-index that are applicable here.

Report this publication

Statistics

Seen <100 times