‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

This extended abstract is a summary of the main results in [4]. We consider a stability result for the inverse problem associated with the Sturm-Liouville equation −y′′ + q0(x)y = λy, x ∈ (0, 1), in which the potential q0 ∈ L(0, 1) is allowed to be complex-valued and the spectral data consists of the firstN Dirichlet-Dirichlet eigenvalues and the firstN Dirichlet-Neumann eigenvalues, determined...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

We discuss direct and inverse spectral theory of self-adjoint Sturm– Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl–Titchmarsh theory for these relations. Consequently, we apply de Branges’ subspace ordering theorem to obtain inverse uniqueness results for the associated spectral measure. The results can be applied to...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...