Basis properties of the root functions of an eigenvalue problem with a spectral parameter in the boundary conditions (Q600753)

Consider boundary conditions of a two-point boundary value problem governing the stability in vibrations of a homogeneous loaded string, depending, beside the spectral parameter, on two other real parameters, denoted by \(a\) and \(b\), respectively. The analytical results obtained here for \(a>0\), \(b<0\) concern basis properties of the root functions of the eigenvalue problem defined by a non-self-adjoint closed operator with compact resolvent.