Solvability of a Boundary Value Problem for Second-Order Elliptic Differential Operator Equations with a Spectral Parameter in the Equation and in the Boundary Conditions

In a Hilbert space H, we study noncoercive solvability of a boundary value problem for second-order elliptic differential-operator equations with a spectral parameter in the equation and in the boundary conditions in the case where the leading part of one of the boundary conditions contains a bounded linear operator in addition to the spectral parameter. We also illustrate applications of the general results obtained to elliptic boundary value problems.