Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 185-206

A degree theory for a class of perturbed Fredholm maps

Pierluigi Benevieri,1 Alessandro Calamai,2 and Massimo Furi1

1Dipartimento di Matematica Applicata “Giovanni Sansone,”, Università degli Studi di Firenze, 3 via S. Marta,, Firenze 50139, Italy
2Dipartimento di Matematica “Ulisse Dini,”, Università degli Studi di Firenze, 67/A viale G. B. Morgagni, Firenze 50134, Italy

Received 26 October 2004

Copyright © 2005 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.


We define a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between infinite-dimensional real Banach spaces. Our notion extends the degree introduced by Nussbaum for locally α-contractive perturbations of the identity, as well as the recent degree for locally compact perturbations of Fredholm maps of index zero defined by the first and third authors.