Electron. J. Differential Equations, Vol. 2017 (2017), No. 41, pp. 1-7.

An inverse Sturm-Liouville problem with a generalized symmetric potential

Esin Inan Eskitascioglu, Mehmet Acil

Abstract:
We consider the normal form of Sturm-Liouville differential equations with separable boundary conditions. For this problem we know that the potential function is determined uniquely by two spectra and that if the potential is symmetric, then it is determined uniquely by just one spectrum. In this paper firstly we generalize symmetric potential and then investigate change of needed data to determine potential function uniquely.

Submitted December 22, 2016. Published February 7, 2017.
Math Subject Classifications: 31A25, 34B24, 34L16.
Key Words: Boundary value and inverse problems; Sturm-Liouville theory; numerical approximation of eigenvalues.

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Esin Inan Eskitascioglu
Department of Mathematics
Faculty of Sciences, Yuzuncu Yil University
65080, Van, Turkey
email: inancinar@mynet.com
Mehmet Acil
Department of Mathematics
Faculty of Sciences, Yuzuncu Yil University
65080, Van, Turkey
email: mehmetacil76@gmail.com

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