Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

We study the equation −Δgw+w=λα(σ)f(w) on a d-dimensional homogeneous Cartan-Hadamard Manifold M with d≥3. Without using the theory of topological indices, we prove the existence of infinitely many solutions for a class of nonlinearities f which have an oscillating behavior either at zero or at infinity.