A boundary value problem for the Dirac system with a spectral parameter in the boundary conditions
Consider the following boundary value problem for the Dirac system with the same spectral parameter in the equations and in the boundary conditions \[ u'-(\lambda+P(x))w=0,\quad w'+(\lambda+R(x))u=0, \] \[ (\lambda\cos\alpha+a_0)u(0)-(\lambda\sin\alpha+b_0)w(0)=0, \] \[ (\lambda\cos\beta+a_1)u(1)-(\lambda\sin\beta+b_1)w(1)=0; \] here, \(0\leq x\leq1\), \(\lambda\) is the spectral parameter, \(P\) and \(R\) are real-valued functions from the class \(C[0,1]\), \(a_k,b_k\) are real parameters, and \(\alpha,\beta\in[-\pi/2;\pi/2]\). Main results of this article are concerned with the oscillation property of eigenfunctions and asymptotic formulas for the eigenvalues.
scientific article; zbMATH DE number 1916023