On the Brezis-Nirenberg problem for the $(p,q)$-Laplacian

TL;DR

This paper investigates the existence and nonexistence of solutions for critical $(p,q)$-Laplacian problems in bounded domains, extending previous results to more general cases.

Contribution

It provides new existence and nonexistence results for the critical $(p,q)$-Laplacian problem, broadening the understanding beyond classical models.

Findings

Established conditions for existence of solutions.

Identified scenarios where solutions do not exist.

Extended previous results to more general $(p,q)$-Laplacian cases.

Abstract

We prove some existence and nonexistence results for a class of critical $(p,q)$-Laplacian problems in a bounded domain. Our results extend and complement those in the literature for model cases.