Abstract and Applied Analysis
Volume 2006 (2006), Article ID 64764, 20 pages
A degree theory for locally compact perturbations of Fredholm maps in Banach spaces
Dipartimento di Matematica Applicata G. Sansone, Via S. Marta 3, Firenze 50139, Italy
Received 16 December 2003; Accepted 21 January 2005
Copyright © 2006 Pierluigi Benevieri and Massimo Furi. 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 present an integer valued degree theory for locally compact
perturbations of Fredholm maps of index zero between (open sets
in) Banach spaces (quasi-Fredholm maps, for short). The
construction is based on the Brouwer degree theory and on the
notion of orientation for nonlinear Fredholm maps given by the
authors in some previous papers. The theory includes in a natural
way the celebrated Leray-Schauder degree.