On impulsive Sturm–Liouville operators with singularity and spectral parameter in boundary conditions

Abstract

We study properties and the asymptotic behavior of spectral characteristics for a class of singular Sturm-Liouville differential operators with discontinuity conditions and an eigenparameter in boundary conditions. We also determine the Weyl function for this problem and prove uniqueness theorems for a solution of the inverse problem corresponding to this function and spectral data. Дослiджено властивостi та асимптотичну поведiнку спектральних характеристик для класу сингулярних диференцiальних операторiв Штурма-Лiувiлля з розривними умовами та власним параметром у граничних умовах. Визначено функцiю Вейля для цiєї задачi та доведено теореми про єдинiсть розв'язку оберненої задачi, що вiдповiдає цiй функцiї та спектральним даним.

Solvability of the inverse spectral problem for Sturm-Liouville operator with spectral parameter in the boundary condition

“…4) Recover function ( 18) from (20). 5) Find the values of the function ( 19) at points λ k using (22). 6) Recover function ( 23) by interpolation formula (24).…”

“…Such problems also arise in technical physics, mechanics, acoustics of flow channels, electrodynamics, and other areas [11], [36], [49]. In the case of separated boundary conditions, some variants of such problems are completely solved (see [5]- [7], [9], [10], [15]- [18], [22], [28], [42], [50]). Little studied are the boundary value problems in the case when the nonseparated boundary conditions depend on the spectral parameter.…”

The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators

“…These types of problems are especially encountered in heat and mass transfer problems ( [17]). There are many studies on this subject in the literature [2,6,7,8,9,12,13,14,19,23].…”

On a lipschitz stability problem for p-Laplacian Bessel equation

“…Later, many researchers obtained some important results for di¤erent type operators. Inverse eigenvalue problem for classical Bessel equation was studied by various authors (see [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]). …”