On a boundary problem generated by a self-adjoint Sturm–Liouville differential operator on the entire real axis

In Hilbert space $L^2(0,a)$, $0<a<infty$, we consider the spectral problem generated by a Sturm–Liouville operator with real potential and boundary conditions which depend on the spectral parameter. The paper investigates the spectrum and the questions connected with the completeness of the system of eigenfunctions.