Equality in Wielandt’s eigenvalue inequality
Shmuel Friedland (2015)
Special Matrices
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In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
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Equality in Wielandt’s eigenvalue inequality
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Jan Bochenek (1980)
Annales Polonici Mathematici
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Behrouz Emamizadeh, Amin Farjudian (2014)
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In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...
Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.
Eberhard, W., Freiling, G., Schneider, A. (1992)
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Ivo Marek (1964)
Matematicko-fyzikálny časopis
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J. Fleckinger, J. Hernández, F. Thélin (2004)
Bollettino dell'Unione Matematica Italiana
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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
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Jan Bochenek (1971)
Annales Polonici Mathematici
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A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...