A note on the Nonlinear Schrödinger Equation on Cartan-Hadamard manifolds with unbounded and vanishing potentials.

We study the semilinear equation-Δ_gu+V(σ)u = f(u) on a Cartan-Hadamard manifold Μ of dimension N ≥ 3, and we prove the existence of a nontrivial solution under suitable assumptions on the potential function V ε C(Μ). In particular, the decay of V at infinity is allowed, with some restrictions related to the geometry of Μ. We generalize some results proved in R^N by Alves et al. [ABSTRACT FROM AUTHOR]