A note on the NLS equation on Cartan-Hadamard manifolds with unbounded and vanishing potentials

Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi

We study the semilinear equation $-{\Delta }_{g}u+V(\sigma )u=f(u)$ on a Cartan-Hadamard manifold $\mathcal{M}$ of dimension $N\ge 3$, and we prove the existence of a nontrivial solution unde…