Spectral properties for a system of Dirac equations with nonlinear dependence on the spectral parameter

Abstract

We consider the boundary value problem generated by a system of Dirac equations with polynomials of spectral parameter in the boundary condition. We investigate the continuity of the scattering function and provide Levinson-type formula, which shows that the increment of the scattering function’s logarithm is related to the number of eigenvalues of the boundary value problem.

Keywords

• levinson-type formula
• scattering data
• spectral parameter dependent boundary condition
• 34l25
• 81u40
• 34l40
• 34b07
• 81q10