Spectral properties for discontinuous Dirac system with eigenparameter‐dependent boundary condition

Abstract

In this paper, Dirac system with interface conditions and spectral parameter dependent boundary conditions is investigated. By introducing a new Hilbert space, the original problem is transformed into an operator problem. Then the continuity and differentiability of the eigenvalues with respect to the parameters in the problem are showed. In particular, the differential expressions of eigenvalues for each parameter are given. These results would provide theoretical support for the calculation of eigenvalues of the corresponding problems.