On recovering quadratic pencils with singular coefficients and entire functions in the boundary conditions

Abstract

In the paper, we study an inverse spectral problem for quadratic pencils of Sturm-Liouville operators with singular coefficients and entire functions in the boundary conditions. It is proved that a part of the spectrum is sufficient for recovering the pencil if this part generates a complete functional system. As well, we obtain an algorithm solving the inverse problem and apply the results to studying a partial inverse problem.