Journal of the
Korean Mathematical Society JKMS

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line $\left[ 0, \infty\right)$. In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

Keywords: inverse problem of scattering theory on half line, Sturm-Liouville operator with a nonlinear spectral parameter, scattering data

MSC numbers: Primary 34B07, 34A55, 34B24