Inverse spectral problems for Dirac operator with eigenvalue dependent boundary and jump conditions

Abstract

We deal with the Dirac operator with eigenvalue dependent boundary and jump conditions. Properties of eigenvalues, eigenfunctions and the resolvent operator are studied. Moreover, uniqueness theorems of the inverse problem according to the Weyl functions and the spectral data (the sets of eigenvalues and norming constants; two different eigenvalues sets) are proved.

P-Laplacian Dirac system on time scales

“…Dirac operator which is a modern presentation of the relativistic quantum mechanics of electrons aiming to bring a new mathematical result to a wider audience is the relativistic Schrödinger operator in quantum physics [18][19][20][21][22][23]. There are many studies in spectral theory related to different versions of Dirac system [24][25][26][27][28][29][30][31][32][33][34].…”

Inverse spectral problem for non-selfadjoint Dirac operator with boundary and jump conditions dependent on the spectral parameter

“…In [16], B.Keskin and A.S.Ozkan obtained the uniqueness theorems of inverse spectral problem in the situation that p(x), r(x) are real-valued functions and h i , H i , α, β are real numbers. However, the problem for recovering the potential remains open.…”

On discontinuous Dirac systems with eigenvalue dependent boundary conditions

“…This type of problems may have discontinuities in the solution or its derivative at an inner point of the interval and arise in heat and mass transfer, mechanics, electronics, radio, geophysics and other branches natural sciences. Direct and inverse problems for Dirac differential equation with transmission conditions have been investigated in [4][5][6]. The aim of this paper is to study a Dirac system with transmission condition and eigenparameter in boundary condition.…”