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An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions

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Abstract

The object of this paper is to establish an expansion theorem for a regular right-definite eigenvalue problem with an eigenvalue parameter λ which is contained in the Schrödinger partial differential equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain inR n(n≥2). We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.

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Authors and Affiliations

  1. Mathematics Department Faculty of Science, Zagazig University, Zagazig, Egypt

    Zayed E. M. E.

  2. Mathematics Department Faculty of Science, Ain Shams University, Heliopolis, Cairo, Egypt

    Ibrahim S. F. M.

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  1. Zayed E. M. E.
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  2. Ibrahim S. F. M.
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Zayed, E.M.E., Ibrahim, S.F.M. An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions. Acta Mathematica Sinica 11, 399–407 (1995). https://doi.org/10.1007/BF02248750

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  • DOI: https://doi.org/10.1007/BF02248750

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