Boundary value problems for \(2\times 2\) Dirac type systems with spectral parameter in boundary conditions (Q2754843)

The author considers some problems on the interval \([0,1]\) for the system NEWLINE\[NEWLINE \frac{1}{i}By'+Q(x)y+\int_0^xM(x,t)y(t) dt=\lambda y NEWLINE\]NEWLINE with the spectral parameter in boundary conditions. Here, \(B\) is a diagonal real matrix, \(Q(x)=\left( \begin{smallmatrix} 0&q_1\\ q_2&0\end{smallmatrix} \right)\), \(q_j\in L_1(0,1)\), and \(M\) is a bounded matrix function. Conditions for the completeness of the system of root vectors and some of its subsystems are obtained.