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Oscillation theorems for the Dirac operator with a spectral parameter in the boundary condition. (English) Zbl 1399.34279

Summary: We consider the boundary value problem for the one-dimensional Dirac equation with spectral parameter dependent boundary condition. We give location of the eigenvalues on the real axis, study the oscillation properties of eigenvector-functions and obtain the asymptotic behavior of the eigenvalues and eigenvector-functions of this problem.

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34B09 Boundary eigenvalue problems for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34B07 Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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