Elliptic eigenvalue problems with eigenparameter dependent boundary conditions

Let A be a uniformly elliptic second order linear operator on a smooth bounded domain Omega subset of R-n. We study the eigenvalue problem Au = lambdau subject to boundary conditions B(0)u = lambdaB(1)u on partial derivative Omega, where B-j are linear boundary operators. The problem is recast in the form Au=lambdau 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. (C) 2001 Academic Press.