Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions

Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symm...

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Main Authors: Manfred Möller, Bertin Zinsou
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2013/280970
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author Manfred Möller
Bertin Zinsou
author_facet Manfred Möller
Bertin Zinsou
author_sort Manfred Möller
collection DOAJ
description Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.
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institution OA Journals
issn 0972-6802
1758-4965
language English
publishDate 2013-01-01
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series Journal of Function Spaces and Applications
spelling doaj-art-74bb5ce3e26d4b4881d367a52ba2b2592025-08-20T02:07:20ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/280970280970Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary ConditionsManfred Möller0Bertin Zinsou1The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaThe John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaConsidered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.http://dx.doi.org/10.1155/2013/280970
spellingShingle Manfred Möller
Bertin Zinsou
Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
Journal of Function Spaces and Applications
title Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
title_full Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
title_fullStr Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
title_full_unstemmed Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
title_short Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
title_sort asymptotics of the eigenvalues of a self adjoint fourth order boundary value problem with four eigenvalue parameter dependent boundary conditions
url http://dx.doi.org/10.1155/2013/280970
work_keys_str_mv AT manfredmoller asymptoticsoftheeigenvaluesofaselfadjointfourthorderboundaryvalueproblemwithfoureigenvalueparameterdependentboundaryconditions
AT bertinzinsou asymptoticsoftheeigenvaluesofaselfadjointfourthorderboundaryvalueproblemwithfoureigenvalueparameterdependentboundaryconditions