Boundary Value Problems
Volume 2010 (2010), Article ID 171967, 17 pages
Research Article

On an Inverse Scattering Problem for a Discontinuous Sturm-Liouville Equation with a Spectral Parameter in the Boundary Condition

Mathematics Department, Science and Letters Faculty, Mersin University, 33343 Mersin, Turkey

Received 9 April 2010; Accepted 22 May 2010

Academic Editor: Michel C. Chipot

Copyright © 2010 Khanlar R. Mamedov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An inverse scattering problem is considered for a discontinuous Sturm-Liouville equation on the half-line [0,) with a linear spectral parameter in the boundary condition. The scattering data of the problem are defined and a new fundamental equation is derived, which is different from the classical Marchenko equation. With help of this fundamental equation, in terms of the scattering data, the potential is recovered uniquely.