Open Access

Bifurcation Results for a Class of Perturbed Fredholm Maps

Fixed Point Theory and Applications20082008:752657

https://doi.org/10.1155/2008/752657

Received: 3 March 2008

Accepted: 27 July 2008

Published: 31 July 2008

Abstract

We prove a global bifurcation result for an equation of the type , where is a linear Fredholm operator of index zero between Banach spaces, and, given an open subset of , are and continuous, respectively. Under suitable conditions, we prove the existence of an unbounded connected set of nontrivial solutions of the above equation, that is, solutions with , whose closure contains a trivial solution . The proof is based on a degree theory for a special class of noncompact perturbations of Fredholm maps of index zero, called -Fredholm maps, which has been recently developed by the authors in collaboration with M. Furi.

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Authors’ Affiliations

(1)
Dipartimento di Matematica Applicata, Università degli Studi di Firenze
(2)
Dipartimento di Scienze Matematiche, Università Politecnica delle Marche

Copyright

© P. Benevieri and A. Calamai. 2008

This article is published under license to BioMed Central Ltd. 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.