Sturm–Liouville Problems with Transfer Condition Herglotz Dependent on the Eigenparameter: Eigenvalue Asymptotics

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

“…Through inducting the generalized normal constants they have proved the uniqueness theorem, then a construction method for solving this inverse problem was given [30]. In 2018 and 2021, Bartels et al presented Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter, and showed the Hilbert space formulation of the problem and calculated out the eigenvalue and eigenfunction asymptotic formula on this problem [31] [34]. Zhang et al studied the finite spectrum of Sturm-Liouville problems with both jump conditions dependent on the spectral parameter [35].…”

Inverse nodal problems for singular diffusion equation

“…In the literature [5][6][7][8][9][10][11][12][13], the spectral properties of the operator produced by the regular differential equation given with separated and non-separated boundary conditions containing the spectral parameter were examined and the uniqueness theorems related to the solution of the spectral inverse problem were proved. In previous studies [14][15][16][17], the spectral properties of the operator produced by the Schrödinger equation with the singular coefficient given with the boundary conditions depending on the spectral parameter were examined and the solution of the inverse spectral problems according to different spectral data was given.…”

Matrix Representations for a Class of Eigenparameter Dependent Sturm–Liouville Problems with Discontinuity

“…Recently, Sturm-Liouville problems (SLPs) with discontinuity inside intervals have attracted significant attention from scholars due to their wide application in various fields. For example, one application involves a string loaded with point masses [1][2][3][4][5]. Generally speaking, the eigenparameter only appears in the equation, but in many actual phenomena, it is necessary for the eigenparameter to appear in the boundary conditions, such as heat conduction at the liquid-solid interface [6], and so on.…”

“…In recent years, SLPs with interface conditions dependent on parameters have also captured the attention of researchers, see [2][3][4] and references therein. In reference [2], the author obtained the operator-theoretic formulation.…”

“…In reference [2], the author obtained the operator-theoretic formulation. The asymptotic properties of eigenvalues were given for SLPs with interface conditions that were rationally dependent on the parameters in [3]. In work by Mukhtarov et al [4], Green's function was provided for eigenparameter-dependent SLPs with interface conditions.…”