A maximum of the first eigenvalue of semibounded differential operator with a parameter

We consider a self-adjoint differential operator in Hilbert space. Then the domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “is cleared” from the points of the spectrum of the perturbed operator. For the Sturm–Liouville operator on the segment and the Laplace operator on the square such a possibility is attained cia integral perturbations of boundary conditions.