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 $C^2$.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.