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Abstract
Inverse nodal problems for the Sturm–Liouville equation in a finite interval with boundary conditions depending polynomially on the spectral parameter are studied. We prove a uniqueness theorem: nodal points uniquely determine the polynomials of the boundary conditions and the potential function of the Sturm–Liouville equation. For these inverse nodal problems we provide constructive procedures.
Acknowledgements
The authors would like to thank the referees for valuable comments that improved the original manuscript. The first author would like to thank Prof. V.A. Yurko, Department of Mathematics, Saratov University, Russia, and Prof. G. Freiling, Faculty of Mathematics, University Duisburg-Essen, Germany, for discussions related to some topics of spectral analysis of differential operators. This work was supported by the Natural Science Foundation of Jiangsu Province of China (BK 2010489), the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366), NUST Research Funding (No. AE88787) and the National Natural Science Foundation of China (11071119).