Inverse problem for a quadratic pencil of Sturm–Liouville operator

The purpose of this paper is to solve the inverse problem for a quadratic pencil of Sturm–Liouville operator on a finite interval. By using the Hochstadt's method, it is shown that the potential function can be given from two spectras as uniquely. Later, by generalizing this result, the Hochstadt's theorem which is related to the structure of difference for the potential functions is obtained.