on a uniqueness theorem of sturm–liouville equations with boundary conditions polynomially dependent on the spectral parameter

Abstract Inverse nodal problems for Sturm–Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset WB([a,b]) $W_{B}([a,b])$ can uniquely determine the operator up to a constant translation of eigenparameter and potential, where [a,b] $[a,b]$ is an arbitrary interval which contains the middle point of the domain of the operator and B is a subset of N $\mathbb {N}$ which satisfies some condition (see Theorem 4.2).