Inverse Sturm-Liouville problems with eigenvalue-dependent boundary and discontinuity conditions

Abstract

An impulsive boundary-value problem generated by Sturm-Liouville differential equation with the eigenvalue parameter non-linearly contained in one boundary condition and in the jump conditions is considered. It is shown that the coefficients of the problem is uniquely determined either by the Weyl function or by Prufer's angle. It is also proven that two given spectra uniquely determine the coefficients of the problem.