Electron. J. Diff. Equ., Vol. 2013 (2013), No. 237, pp. 1-9.

Inverse scattering problems for energy-dependent Sturm-Liouville equations with point delta-interaction and eigenparameter-dependent boundary condition

Manaf Dzh. Manafov, Abdullah Kablan

We consider an inverse problem of the scattering theory for energy-dependent Sturm-Liouville equations on the half line $[0,+\infty )$ with point $\delta $-interaction and eigenparameter-dependent boundary condition. We define the scattering data of the problem first, then consider the basic equation and study an algorithm for finding the potentials with the given scattering data.

Submitted July 29, 2013. Published October 24, 2013.
Math Subject Classifications: 34A55, 34B24, 47E05.
Key Words: Inverse scattering; scattering data; point delta-interaction; eigenvalue-dependent boundary condition.

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Manaf Dzh. Manafov
Faculty of Arts and Sciences
Department of Mathematics, Adiyaman University
Adiyaman, 02040, Turkey
email: mmanafov@adiyaman.edu.tr
Abdullah Kablan
Faculty of Arts and Sciences
Department of Mathematics, Gaziantep University
Gaziantep, 27310, Turkey
email: kablan@gantep.edu.tr

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