Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 27154, 20 pages

A degree theory for a class of perturbed Fredholm maps II

Pierluigi Benevieri,1 Alessandro Calamai,2 and Massimo Furi1

1Dipartimento di Matematica Applicata “G. Sansone”, Via S. Marta 3, Firenze 50139, Italy
2Dipartimento di Matematica “U. Dini”, Viale G.B. Morgagni 67/A, Firenze 50134, Italy

Received 30 June 2005; Revised 10 October 2005; Accepted 24 October 2005

Copyright © 2006 Pierluigi Benevieri et al. 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.


In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local α-condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.