The interior inverse problem for the impulsive Sturm–Liouville equation

On the determination of the quadratic pencil of the Sturm-Liouville operator with an impulse

“…Inverse problems of spectral analysis consist in the recovery of operators from their spectral data such as the spectrum, the normalizing constants, the Weyl function, the spectral function, and the nodal points. The most account of this theory and its applications can be found in mathematics, mathematical physics, electronics, quantum mechanics, geophysics, etc (see [2,3,6,8,9,10,11,14,19,23] for more details).…”

“…In theses studies, interior inverse problems for Sturm-Liouville operators as an efficient method have been investigated by authors in recent years. This method is studied considering the property of the eigenfunctions in the mid point of the interval and an arbitrary point in the first or second half of the interval [6,18,19,22]. Half inverse problems are also used for the reconstruction of the operator by one spectrum and known potentials on the half of the interval [3,9,21].…”