Abstract
This paper deals with a Dirac system with transmission condition and eigenparameter in boundary condition. We give an operator-theoretic formulation of the problem then investigate the existence of the solution. Some spectral properties of the problem are studied.
Highlights
After Walter [1] had given an operator-theoretic formulation of eigenvalue problems with eigenvalue parameter in the boundary conditions, Fulton [2, 3] has carried over the methods of Titchmarsh [4, chapter 1] to this problem
The existence of solution and some spectral properties of Sturm-Liouville problem with eigenparameter-dependent boundary conditions and with transmission conditions at one or more inner points of considered finite interval has been studied by Mukhtarov and Tunc [5]; see [6, 7]
A Dirac system when the eigenparameter appears in boundary conditions has been studied by Kerimov [8]
Summary
After Walter [1] had given an operator-theoretic formulation of eigenvalue problems with eigenvalue parameter in the boundary conditions, Fulton [2, 3] has carried over the methods of Titchmarsh [4, chapter 1] to this problem. The existence of solution and some spectral properties of Sturm-Liouville problem with eigenparameter-dependent boundary conditions and with transmission conditions at one or more inner points of considered finite interval has been studied by Mukhtarov and Tunc [5]; see [6, 7]. A Dirac system when the eigenparameter appears in boundary conditions has been studied by Kerimov [8]. The aim of the present paper is to study a Dirac system with transmission condition and eigenparameter in boundary condition. B1u1 (b) − a1u2 (b) + λ (sin βu (b) − cos βu (b)) = 0, (5) and transmission conditions at the inner point x = c u1 (c − 0) = γu (c + 0) , (6).
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