A characterization related to Schrödinger equations on Riemannian manifolds

Francesca Faraci, Csaba Farkas

In this paper we consider the following problem $$\begin{cases} -Δ_{g}u+V(x)u=λα(x)f(u), & \mbox{in }M\\ u\geq0, & \mbox{in }M\\ u\to0, & \mbox{as }d_{g}(x_{0},x)\to\infty \end{cas…