We give necessary as well as sufficient conditions for a unit $0$-eigenvector of bounded linear operator $A$ between Banach spaces to be a bifurcation point for the unit eigenvectors of $A + epsilon B$. These conditions turn out to be particularly meaningful when the perturbing operator $B$ is linear. Moreover, since our sufficient condition is trivially satisfied when the kernel of $A$ is one-dimensional, we extend a result of the first author, under the additional assumption that $B$ is of class $C^2$.

Normalized Eigenvectors of a Perturbed Linear Operator via General Bifurcation / R. Chiappinelli; M. Furi; M. Pera. - In: GLASGOW MATHEMATICAL JOURNAL. - ISSN 0017-0895. - STAMPA. - 50:(2008), pp. 303-318. [10.1017/S0017089508004217]

Normalized Eigenvectors of a Perturbed Linear Operator via General Bifurcation

FURI, MASSIMO;PERA, MARIA PATRIZIA
2008

Abstract

We give necessary as well as sufficient conditions for a unit $0$-eigenvector of bounded linear operator $A$ between Banach spaces to be a bifurcation point for the unit eigenvectors of $A + epsilon B$. These conditions turn out to be particularly meaningful when the perturbing operator $B$ is linear. Moreover, since our sufficient condition is trivially satisfied when the kernel of $A$ is one-dimensional, we extend a result of the first author, under the additional assumption that $B$ is of class $C^2$.
2008
50
303
318
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R. Chiappinelli; M. Furi; M. Pera
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/252543
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