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$%Z. Djadli, Nonlinear elliptic equations involving critical Sobolev exponent on compact Riemannian manifolds in presence of symmetries, Rev. Mat. Complut. 12 (1999), no. 1, 201–229. %$

In this paper, we study a nonlinear elliptic equation with critical exponent, invariant under the action of a subgroup 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 , we show that we can solve this equation for supercritical exponents.

1991 Mathematics Subject Classification: 58G03, 35J60.