An expansion theorem for regular elliptic eigenvalue problem with eigenvalue parameter in the boundary conditions

The object of this paper is to establish the expansion theorem for a regular elliptic eigenvalue problem of a general multiply connected bounded domain in R-m, (m greater than or equal to 2), where the eigenvalue parameter lambda is contained in the elliptic partial differential equation and in the general type of boundary conditions. We associated with this problem an essentially self-adjoint operator A in a suitably defined Hilbert space H and then we develop an associated eigenfunction expansion theorem. (C) 2003 Elsevier Inc. All rights reserved.