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A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter
Author(s) -
Voss Heinrich
Publication year - 2009
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.670
Subject(s) - mathematics , eigenvalues and eigenvectors , minimax , hilbert space , differentiable function , nonlinear system , mathematical analysis , class (philosophy) , operator (biology) , variational method , mathematical optimization , computer science , physics , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , transcription factor , gene
Variational characterizations of real eigenvalues of selfadjoint operators on a Hilbert space depending nonlinearly on an eigenparameter usually assume differentiable dependence of the operator on the eigenparameter. In this paper we generalize these results to nonlinear problems that depend only continuously on the parameter. This result is applied to a class of variational eigenvalue problems that in particular contains the vibrations of plates with attached masses. Copyright © 2009 John Wiley & Sons, Ltd.