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.

In this paper, p-biharmonic equations involving Hardy potential and negative exponents with a parameter λ are considered. By means of the structure and properties of Nehari manifold, we give uniform lower bounds for Λ > 0, which is the supremum of the set of λ. When λ ∈ (0, Λ), the above problems admit at least two positive solutions.