Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 185-206
doi:10.1155/FPTA.2005.185
A degree theory for a class of perturbed Fredholm maps
Pierluigi Benevieri1
, Alessandro Calamai2
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
Abstract
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.