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
Boundary Value Problems 2010, 2010:171967 doi:10.1155/2010/171967Published: 21 June 2010
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.