Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable

We consider ihe differential expression M [y]: = −y″ + qy on [0, ∞) where q _∈ L p [0, ∞) for some p ≧ 1. It is known that M , together with the boundary conditions y (0) = 0 or y ′(0) = 0, defines linear operators on L 2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the L p norm of q _ and extend results of Everitt and Veling.