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

Abstract

We study the semilinear equation on a Cartan‐Hadamard manifold of dimension , and we prove the existence of a nontrivial solution under suitable assumptions on the potential function . In particular, the decay of at infinity is allowed, with some restrictions related to the geometry of . We generalize some results proved in by Alves et al.