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[0,1], and Dirichlet or Neumann–Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential from these two spectra.
doi:10.1016/j.jfa.2007.10.007 
Copyright © 2007 Elsevier Inc. All rights reserved.
Received 24 July 2007;
accepted 25 October 2007.
Communicated by L. Gross.
Available online 28 November 2007.
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Abstract
We extend relative oscillation theory to the case of Sturm–Liouville operators Hu=r−1(−(pu′)′+qu) with different p's. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.
Keywords: Sturm–Liouville operators; Oscillation theory; Spectral shift function
