Uniqueness of the solution of the inverse problem of scattering theory for the Sturm-Liouville operator with a spectral parameter in the boundary condition. (Q1889516)

The inverse scattering problem is solved for the Sturm-Liouville equation \[ -y''+q(x)y=\lambda^2 y,\; x>0,\; (1+x)q(x)\in L(0,\infty), \] with the boundary condition \(y'(0)=(a_0+ia_1\lambda+a_2\lambda^2)y(0)=0\), where \(q(x)\) and \(a_0\) are real, and \(a_1\geq 0,\, a_2>0\).