  We investigate a large class of elliptic differential inclusions on
non-compact complete Riemannian manifolds which involves the Laplace-Beltrami
operator and a Hardy-type singular term. Depending on the behavior of the
nonlinear term and on the curvature of the Riemannian manifold, we guarantee
non-existence and existence/multiplicity of solutions for the studied
differential inclusion. The proofs are based on nonsmooth variational analysis
as well as isometric actions and fine eigenvalue properties on Riemannian
manifolds. The results are also new in the smooth setting.
