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