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Axioms 2018, 7(2), 39; https://doi.org/10.3390/axioms7020039

What Do You Mean by “Nonlinear Eigenvalue Problems”?

Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, I-53100 Siena, Italy
Received: 30 March 2018 / Revised: 5 June 2018 / Accepted: 6 June 2018 / Published: 9 June 2018
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Abstract

A nonlinear eigenvalue problem is generally described by an equation of the form F(λ,x)=0, where F(λ,0)=0 for all λ, and contains by definition two unknowns: the eigenvalue parameter λ and the “nontrivial” vector(s) x corresponding to it. The nonlinear dependence of F can be in either of them (and of course in both), and also the research in this area seems to follow two quite different directions. In this review paper, we try to collect some points of possible common interest for both fields. View Full-Text
Keywords: eigenspace; algebraic multiplicity; bifurcation; bifurcation eigenspace; algebraic multiplicity; bifurcation; bifurcation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chiappinelli, R. What Do You Mean by “Nonlinear Eigenvalue Problems”? Axioms 2018, 7, 39.

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