BOUNDS ON THE FIRST NONZERO EIGENVALUE FOR SELF-ADJOINT BOUNDARY VALUE PROBLEMS ON NETWORKS

We aim here at obtaining bounds on the first nonzero eigenvalue for selfadjoint boundary value problems on a weighted network by means of equilibrium measures, that include the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some...

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Bibliographic Details
Published inApplicable analysis and discrete mathematics Vol. 2; no. 1; pp. 92 - 106
Main Authors Bendito, E., Carmona, A., Encinas, A. M., Gesto, J. M.
Format Journal Article
LanguageEnglish
Published University of Belgrade, Faculty of Electrical Engineering Academic Mind 01.04.2008
Subjects
Adjoints
Boundary value problems
Connectivity
Eigenfunctions
Eigenvalues
Laplacians
Mathematical functions
Mathematical inequalities
Vertices
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Summary:We aim here at obtaining bounds on the first nonzero eigenvalue for selfadjoint boundary value problems on a weighted network by means of equilibrium measures, that include the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some examples. In particular we emphasize the case of distance-regular graphs and we show that the obtained bounds are better than those known until now.
ISSN:1452-8630
2406-100X
DOI:10.2298/AADM0801092B