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Inverse transmission eigenvalue problems with the twin-dense nodal subset

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Published/Copyright: July 12, 2016

Abstract

The inverse nodal problem for the Sturm–Liouville operator L(q,a) arisen from acoustic scattering problems was considered. The authors showed that q(x) on the interval [0,1] can be uniquely determined by the interior twin-dense nodal subset WT([0,1]), or WT([a0,1]), respectively. Using the above results, two uniqueness theorems of the spherically symmetric speed of sound η(r) for acoustic scattering problems are obtained.

Acknowledgements

The authors would like to express their gratitude to anonymous referees and Professor V. A. Yurko, Department of Mathematics, Saratov University, Russia, for careful examination and valuable suggestions, which obviously improved the original manuscript.

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Received: 2016-3-22
Revised: 2016-5-18
Accepted: 2016-5-27
Published Online: 2016-7-12
Published in Print: 2017-4-1

© 2017 by De Gruyter

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