Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions (Q522945)

The inverse spectral problem is studied for the boundary value problem \[ y''(r)+k^2 \eta(r)y(r)=0,\; r\in(0,1), \] \[ y(0)=0,\; ay'(0)\frac{\sin k}{k}+y(1)\Big(\cos k+(a-1)\frac{\sin k}{k}\Big)=0, \] where \(a\leq 1.\) The uniqueness theorem is proved, and an algorithm for constructing the solution of the inverse problem is obtained.