Isometry-invariant solutions to a critical problem on non-compact Riemannian manifolds

We analyse an elliptic equation with critical growth set on a d-dimensional (d≥3) Hadamard manifold (M,g). By adopting a variational perspective, we prove the existence of non-zero non-negative solutions invariant under the action of a specific family of isometries. Our result remains valid when the original nonlinearity is singularly perturbed