Ghomari, Mohammed Tewfik2024-09-232024-09-232024-06-19https://dspace.univ-tlemcen.dz/handle/112/23061In 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.enRiemannian manifolds, Yamabe equation, p-Laplacian, Sobolev exponent, Hardy potential, blow up analysis, bubbles.Thesis