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Spectral Asymptotics of Self-Adjoint Fourth Order Differential Operators with Eigenvalue Parameter Dependent Boundary Conditions

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Abstract

A fourth-order regular ordinary differential operator with eigenvalue dependent boundary conditions is considered. This problem is realized by a quadratic operator pencil with self-adjoint operators. The location of the eigenvalues is discussed and the first four terms of the eigenvalue asymptotics are evaluated explicitly.

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Authors and Affiliations

  1. The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    Manfred Möller & Bertin Zinsou

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  1. Manfred Möller
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  2. Bertin Zinsou
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Correspondence to Manfred Möller.

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Communicated by Guest Editors L. Littlejohn and J. Stochel.

Dedicated to Prof. Franciszek Szafraniec on the occasion of his 70th birthday.

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Möller, M., Zinsou, B. Spectral Asymptotics of Self-Adjoint Fourth Order Differential Operators with Eigenvalue Parameter Dependent Boundary Conditions. Complex Anal. Oper. Theory 6, 799–818 (2012). https://doi.org/10.1007/s11785-011-0162-1

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  • DOI: https://doi.org/10.1007/s11785-011-0162-1

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