In this paper we present a new method for proving the existence of an eigenvalue below the essential spectrum for Sturm-Liouville operators with coefficients which are L1 perturbations of periodic functions. This method combines operator theory and “standard” numerical analysis with interval arithmetic analysis. We illustrate the method by showing that the SturmLiouville problem (SLP) consistin...

For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2 2 R and if u1,2 solve the differential equation Huj = Ejuj, j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E1,E2)(H) of H equals the number of zeros of the Wronskian of u1 and u2.