New multiplicity results for critical $p$-Laplacian problems

TL;DR

This paper establishes new multiplicity results for the critical p-Laplacian problem using an innovative critical point theorem that relaxes compactness requirements, advancing understanding in nonlinear PDEs.

Contribution

Introduces a novel abstract critical point theorem involving the Z2-cohomological index, enabling multiplicity results for p-Laplacian problems with weaker compactness assumptions.

Findings

Proves multiple solutions for the Brezis-Nirenberg problem with p-Laplacian.

Develops a new critical point theorem reducing compactness constraints.

Enhances methods for nonlinear elliptic PDEs.

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.