Open Access Research Article

Bifurcation Results for a Class of Perturbed Fredholm Maps

Pierluigi Benevieri1* and Alessandro Calamai2

Author Affiliations

1 Dipartimento di Matematica Applicata, Università degli Studi di Firenze, Via S. Marta 3, 50139 Firenze, Italy

2 Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy

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Fixed Point Theory and Applications 2008, 2008:752657  doi:10.1155/2008/752657


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2008/1/752657


Received: 3 March 2008
Revisions received: 18 July 2008
Accepted: 27 July 2008
Published: 31 July 2008

© 2008 The Author(s).

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.

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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