Inverse problem for a quadratic pencil of Sturm-Liouville operator (Q633659)

The author considers the inverse problem for a quadratic pencil of Sturm-Liouville problem: \[ -y^{\prime \prime }=(q(x)+2\lambda p(x))y=\lambda ^{2}y \] with the boundary conditions \[ y(0,\lambda )=1,\;\;\;y^{\prime }(0,\lambda )=0, \;\;\;y^{\prime }(\pi ,\lambda )+Hy(\pi ,\lambda )=0, \] where \(p,q\in L^{2}[0,\pi ]\) and \(H\) is real. A uniqueness theorem is proved and a Hochstadt-type formula is obtained for this inverse problem.