A uniqueness theorem from partial transmission eigenvalues and potential on a subdomain

It is well known that a spherically symmetric wave speed problem in a bounded spherical region may be reduced, by means of Liouville transform, to the Sturm–Liouville problem L(q) in a finite interval. In this work, a uniqueness theorem for the potential q of the derived Sturm–Liouville problem L(q) is proved when the data are partial knowledge of the given spectra and the potential. Copyright © 2016 John Wiley & Sons, Ltd.