The inverse spectral problem of some singular version of one-dimensional Schrödinger operator with explosive factor in finite interval

The inverse spectral problem is investigated for some singular version of one-dimensional Schrödinger operator with explosive factor on finite interval [0,π][0,π]. In the present paper the explosive factor subdivides the problem into two parts, with different characteristic, which causes a lot of analytical difficulties. We define the spectral data of the problem, derive the main integral equation and show that the potential is uniquely recovered for both parts of the problem.