On the pure critical exponent problem for the p-Laplacian

The aim of the present paper is to prove existence and multiplicity of positive and sign-changing solutions for the pure critical exponent problem for the p-Laplacian operator with Dirichlet boundary conditions on a domain having a nontrivial topology, and discrete symmetry. Pioneering works related to the case p = 2 are H. Brezis and L. Nirenberg [14], J.-M. Coron [5], and A. Bahri and J.-M. Coron [12]. A global compactness analysis for the Palais-Smale sequences is given.