Hardy-Sobolev equations in p-Laplacian on compact Riemannian manifolds.

Abstract

In this thesis we study, on compact Riemannian manifolds, a quasi-linear elliptic equation in p-Laplacian operator containing a Hardy term and a critical Sobolev exponent. We first show that Palais-Smale sequences of our equation are submitted to the well known Struwe decomposition formulas. In a second part, we prove some existence results relying on the decomposition results.