Some Schroedinger operators with power-decaying potentials and pure point spectrum

We construct (deterministic) potentials V(x)=O(x-c) such that the Schroedinger equation -y''+Vy=Ey on x element of [0,∞) has a dense pure point spectrum in (0,∞) for almost all boundary conditions at x=0. As a by-product, we also obtain power-decaying potentials for which the spectrum is purely singular continuous on (0,∞) for all boundary conditions. (orig.)