A uniqueness theorem for inverse eigenparameter dependent Sturm - Liouville problems

and

Published under licence by IOP Publishing Ltd
, , Citation Patrick J Browne and B D Sleeman 1997 Inverse Problems 13 1453 DOI 10.1088/0266-5611/13/6/003

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1 Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon SK S7N 5E6, Canada

2 Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK

Dates

  1. Received 6 March 1997

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0266-5611/13/6/1453

Abstract

We consider the regular Sturm - Liouville problem

with boundary conditions

where, initially, . We show that the eigenvalues and appropriately defined norming constants determine the potential q in the sense that two such problems with identical spectra and norming constants must have the same potential. Exceptional cases in which , are also discussed.

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10.1088/0266-5611/13/6/003