Perturbation and spectral theory for singular indefinite Sturm-Liouville operators

in L2((a, b); rj) with endpoints a and bin the limit point case, where, in contrast to the usual assumptions, the weight functions rj have different signs near a and b. In this situation the associated maximal operators become self-adjoint with respect to indefinite inner products and their spectral properties differ essentially from the Hilbert space situation. We investigate the essential spectra and accumulation properties of nonreal and real discrete eigenvalues; we emphasize that here also perturbations of the indefinite weights rj are allowed. Special attention is paid to Kneser type results in the indefinite setting and to L1 perturbations of periodic operators. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).