This paper deals with the inverse spectral problem for a regular Sturm-Liouville problem with boundary conditions depending on the eigenvalue parameter. More exactly, a uniqueness theorem is proved for second order boundary eigenvalue problems
It is assumed that the potential is integrable, , and . It is shown that two problems of the above form for which the eigenvalues and suitable norming constants coincide must have equal potentials. This result is an extension of a well-known theorem of Gel’fand and Levitan for Sturm-Liouville problems with standard boundary conditions to the interesting case of boundary conditions containing the eigenvalue parameter linearly.