Inverse scattering problem for Sturm-Liouville equation with a rational function of spectral parameter in boundary condition

The inverse scattering problem is analyzed for the Sturm-Liouville equation on the half line [0, ∞) with a rational function of spectral parameter in the boundary condition. The main equation is derived, its solvability is proved and it is presented that the potential is uniquely recovered in terms of the scattering data.