Nonlinear elliptic equations involving critical Sobolev exponent on compact riemannian manifolds in presence of symmetries

Abstract

In this paper, we study a nonlinear elliptic equation with critical exponent, invariant under the action of a subgroup G of the isometry group of a compact riemannian manifold. We obtain some existence results of positive solutions of this equation, and under some assumptions on G, we show that we can solve this equation for supercritical exponents.