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An expansion theorem for regular elliptic eigenvalue problem with eigenvalue parameter in the boundary conditions. (English) Zbl 1042.35037

Summary: 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 \(\mathbb{R}^m\), (\(m \geqslant 2\)), where the eigenvalue parameter \(\lambda\) is contained in the elliptic partial differential equation and in the general type of boundary conditions. We associate 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.

MSC:

35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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