Elliptic Eigenvalue Problems with Eigenparameter Dependent Boundary Conditions

Let A be a uniformly elliptic second order linear operator on a smooth bounded domain Ω n. We study the eigenvalue problem Au=λu subject to boundary conditions B0u=λB1u on ∂Ω, where Bj are linear boundary operators. The problem is recast in the form u=λu in a Hilbert or Krein space, and results are given on the location and type of the spectrum, full- and half-range completeness, and regularity of critical points.