New multiplicity results for critical $p$-Laplacian problems

Abstract

We prove new multiplicity results for the Brezis-Nirenberg problem for the $p$-Laplacian. Our proofs are based on a new abstract critical point theorem involving the ${\mathbb{Z}}_2$-cohomological index that requires less compactness than the (PS) condition.

arXiv admin note: text overlap with arXiv:2102.09131