Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent

Abstract

Abstract In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.

Keywords

• quasi-linear elliptic problems
• Nehari manifold
• positive solution
• best Sobolev constant