Inverse problem for Sturm-Liouville operator with complex-valued weight and eigenparameter dependent boundary conditions (Q6626987)

Two inverse problems formulated for the Sturm-Liouville equation \N\[\N-y''+q(x)y=\lambda r(x) y, \quad x \in [0,T] \backslash {\{b\}}\N\]\Nwith \(\lambda\)-dependent boundary conditions and a jump condition at \(x=b\), generated by the complex-valued weight \(r(x)\) discontinuous at \(x=b\), are investigated.\N\NAlthough it is mentioned that this model is related to applications in electronics for constructing parameters of heterogeneous electronic lines with desirable technical characteristics, it would have been interesting and useful if this mathematical modelling investigation would have been derived in some detail from physical principles and practical reasoning.\N\NAs it stands, the paper establishes uniqueness results for the proposed mathematical inverse Sturm-Liouville problems, namely: it is proved that the potential on the whole interval along with some of the constants present in the Robin boundary conditions are uniquely determined by either the Weyl function or by two spectra of eigenvalues.