On a class of critical $N$-Laplacian problems

Tsz Chung Ho, Kanishka Perera

Published 2021-11-23, updated 2022-05-16Version 2

We establish some existence results for a class of critical $N$-Laplacian problems in a bounded domain in ${\mathbb R}^N$. In the absence of a suitable direct sum decomposition, we use an abstract linking theorem based on the ${\mathbb Z}_2$-cohomological index to obtain a nontrivial critical point.