On Some Spectral Problems for Sturm–Liouville Equation With Operator Coefficients

ABSTRACT We offer a detailed treatment of minimal, maximal, dissipative, accumulative, and self‐adjoint operator realizations with exit from space of boundary value problem for the Sturm–Liouville equation with unbounded operator coefficient having discrete spectrum and with boundary condition dependent on the Herglotz–Nevanlinna function of eigenparameter. We also study self‐adjoint operator realizations having purely discrete spectrum or having continuous spectrum which coincide with any interval on real axis. That is done in terms of boundary conditions. In addition, in particular case, we obtain asymptotics of spectrum of self‐adjoint operators with discrete spectrum.