On discontinuous Dirac operator with eigenparameter dependent boundary and two transmission conditions

Yalçın Güldü

doi:10.1186/s13661-016-0639-y

Abstract

In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and eigenfunctions. Then we investigate the Green’s function, the resolvent operator, and some uniqueness theorems by using the Weyl function and some spectral data.

Highlights

Inverse problems of spectral analysis recover operators by their spectral data
Studies of eigenvalue dependence appearing in the differential equation and in the boundary conditions have increased in recent years
Direct and inverse problems for Sturm-Liouville and Dirac operators with transmission conditions are investigated in some papers

Summary

Introduction

Inverse problems of spectral analysis recover operators by their spectral data. Fundamental and vast studies about the classical Sturm-Liouville, Dirac operators, Schrödinger equation, and hyperbolic equations are well studied (see [ – ] and references therein).Studies of eigenvalue dependence appearing in the differential equation and in the boundary conditions have increased in recent years (see [ – ] and corresponding bibliography). The aim of the present paper is to obtain the asymptotic formulas of the eigenvalues and eigenfunctions, to construct the Green’s function and the resolvent operator, and to prove some uniqueness theorems.

Objectives

Results

Conclusion