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

摘要

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 Rm, (m⩾2), where the eigenvalue parameter λ 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.