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Open Access Research

Spectral asymptotics of self-adjoint fourth order boundary value problems with eigenvalue parameter dependent boundary conditions

Manfred Möller* and Bertin Zinsou

Author Affiliations

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

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Boundary Value Problems 2012, 2012:106  doi:10.1186/1687-2770-2012-106

Published: 4 October 2012

Abstract

A regular fourth order differential equation with λ-dependent boundary conditions is considered. For four distinct cases with exactly one λ-independent boundary condition, the asymptotic eigenvalue distribution is presented.

MSC: 34L20, 34B07, 34B08, 34B09.

Keywords:
fourth order boundary value problems; self-adjoint; boundary conditions; eigenvalue distribution; pure imaginary eigenvalues; spectral asymptotics